File: sobol_primitives.cpp

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/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
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 *  * Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
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 *  * Neither the name of NVIDIA CORPORATION nor the names of its
 *    contributors may be used to endorse or promote products derived
 *    from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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/*
 * Portions Copyright (c) 2009 Mike Giles, Oxford University.  All rights
 * reserved.
 * Portions Copyright (c) 2008 Frances Y. Kuo and Stephen Joe.  All rights
 * reserved.
 *
 * Sobol Quasi-random Number Generator example
 *
 * Based on CUDA code submitted by Mike Giles, Oxford University, United Kingdom
 * http://people.maths.ox.ac.uk/~gilesm/
 *
 * and C code developed by Stephen Joe, University of Waikato, New Zealand
 * and Frances Kuo, University of New South Wales, Australia
 * http://web.maths.unsw.edu.au/~fkuo/sobol/
 *
 * For theoretical background see:
 *
 * P. Bratley and B.L. Fox.
 * Implementing Sobol's quasirandom sequence generator
 * http://portal.acm.org/citation.cfm?id=42288
 * ACM Trans. on Math. Software, 14(1):88-100, 1988
 *
 * S. Joe and F. Kuo.
 * Remark on algorithm 659: implementing Sobol's quasirandom sequence generator.
 * http://portal.acm.org/citation.cfm?id=641879
 * ACM Trans. on Math. Software, 29(1):49-57, 2003
 *
 */

#include "sobol_primitives.h"

// Each primitive is stored as a struct where
//  dimension is the dimension number of the polynomial (unused)
//  degree is the degree of the polynomial
//  a is a binary word representing the coefficients
//  m is the array of m values

// The primitives are based on those generated by Stephen Joe and
// Frances Kuo in the joe-kuo-6.10200 set.
// c.f. http://web.maths.unsw.edu.au/~fkuo/sobol/index.html
const struct primitive sobol_primitives[] =
{
    // First dimension is a special case so this entry is actually ignored
    {1, 0, 0, {}},
    {2, 1, 0, {1}},
    {3, 2, 1, {1, 3}},
    {4, 3, 1, {1, 3, 1}},
    {5, 3, 2, {1, 1, 1}},
    {6, 4, 1, {1, 1, 3, 3}},
    {7, 4, 4, {1, 3, 5, 13}},
    {8, 5, 2, {1, 1, 5, 5, 17}},
    {9, 5, 4, {1, 1, 5, 5, 5}},
    {10, 5, 7, {1, 1, 7, 11, 19}},
    {11, 5, 11, {1, 1, 5, 1, 1}},
    {12, 5, 13, {1, 1, 1, 3, 11}},
    {13, 5, 14, {1, 3, 5, 5, 31}},
    {14, 6, 1, {1, 3, 3, 9, 7, 49}},
    {15, 6, 13, {1, 1, 1, 15, 21, 21}},
    {16, 6, 16, {1, 3, 1, 13, 27, 49}},
    {17, 6, 19, {1, 1, 1, 15, 7, 5}},
    {18, 6, 22, {1, 3, 1, 15, 13, 25}},
    {19, 6, 25, {1, 1, 5, 5, 19, 61}},
    {20, 7, 1, {1, 3, 7, 11, 23, 15, 103}},
    {21, 7, 4, {1, 3, 7, 13, 13, 15, 69}},
    {22, 7, 7, {1, 1, 3, 13, 7, 35, 63}},
    {23, 7, 8, {1, 3, 5, 9, 1, 25, 53}},
    {24, 7, 14, {1, 3, 1, 13, 9, 35, 107}},
    {25, 7, 19, {1, 3, 1, 5, 27, 61, 31}},
    {26, 7, 21, {1, 1, 5, 11, 19, 41, 61}},
    {27, 7, 28, {1, 3, 5, 3, 3, 13, 69}},
    {28, 7, 31, {1, 1, 7, 13, 1, 19, 1}},
    {29, 7, 32, {1, 3, 7, 5, 13, 19, 59}},
    {30, 7, 37, {1, 1, 3, 9, 25, 29, 41}},
    {31, 7, 41, {1, 3, 5, 13, 23, 1, 55}},
    {32, 7, 42, {1, 3, 7, 3, 13, 59, 17}},
    {33, 7, 50, {1, 3, 1, 3, 5, 53, 69}},
    {34, 7, 55, {1, 1, 5, 5, 23, 33, 13}},
    {35, 7, 56, {1, 1, 7, 7, 1, 61, 123}},
    {36, 7, 59, {1, 1, 7, 9, 13, 61, 49}},
    {37, 7, 62, {1, 3, 3, 5, 3, 55, 33}},
    {38, 8, 14, {1, 3, 1, 15, 31, 13, 49, 245}},
    {39, 8, 21, {1, 3, 5, 15, 31, 59, 63, 97}},
    {40, 8, 22, {1, 3, 1, 11, 11, 11, 77, 249}},
    {41, 8, 38, {1, 3, 1, 11, 27, 43, 71, 9}},
    {42, 8, 47, {1, 1, 7, 15, 21, 11, 81, 45}},
    {43, 8, 49, {1, 3, 7, 3, 25, 31, 65, 79}},
    {44, 8, 50, {1, 3, 1, 1, 19, 11, 3, 205}},
    {45, 8, 52, {1, 1, 5, 9, 19, 21, 29, 157}},
    {46, 8, 56, {1, 3, 7, 11, 1, 33, 89, 185}},
    {47, 8, 67, {1, 3, 3, 3, 15, 9, 79, 71}},
    {48, 8, 70, {1, 3, 7, 11, 15, 39, 119, 27}},
    {49, 8, 84, {1, 1, 3, 1, 11, 31, 97, 225}},
    {50, 8, 97, {1, 1, 1, 3, 23, 43, 57, 177}},
    {51, 8, 103, {1, 3, 7, 7, 17, 17, 37, 71}},
    {52, 8, 115, {1, 3, 1, 5, 27, 63, 123, 213}},
    {53, 8, 122, {1, 1, 3, 5, 11, 43, 53, 133}},
    {54, 9, 8, {1, 3, 5, 5, 29, 17, 47, 173, 479}},
    {55, 9, 13, {1, 3, 3, 11, 3, 1, 109, 9, 69}},
    {56, 9, 16, {1, 1, 1, 5, 17, 39, 23, 5, 343}},
    {57, 9, 22, {1, 3, 1, 5, 25, 15, 31, 103, 499}},
    {58, 9, 25, {1, 1, 1, 11, 11, 17, 63, 105, 183}},
    {59, 9, 44, {1, 1, 5, 11, 9, 29, 97, 231, 363}},
    {60, 9, 47, {1, 1, 5, 15, 19, 45, 41, 7, 383}},
    {61, 9, 52, {1, 3, 7, 7, 31, 19, 83, 137, 221}},
    {62, 9, 55, {1, 1, 1, 3, 23, 15, 111, 223, 83}},
    {63, 9, 59, {1, 1, 5, 13, 31, 15, 55, 25, 161}},
    {64, 9, 62, {1, 1, 3, 13, 25, 47, 39, 87, 257}},
    {65, 9, 67, {1, 1, 1, 11, 21, 53, 125, 249, 293}},
    {66, 9, 74, {1, 1, 7, 11, 11, 7, 57, 79, 323}},
    {67, 9, 81, {1, 1, 5, 5, 17, 13, 81, 3, 131}},
    {68, 9, 82, {1, 1, 7, 13, 23, 7, 65, 251, 475}},
    {69, 9, 87, {1, 3, 5, 1, 9, 43, 3, 149, 11}},
    {70, 9, 91, {1, 1, 3, 13, 31, 13, 13, 255, 487}},
    {71, 9, 94, {1, 3, 3, 1, 5, 63, 89, 91, 127}},
    {72, 9, 103, {1, 1, 3, 3, 1, 19, 123, 127, 237}},
    {73, 9, 104, {1, 1, 5, 7, 23, 31, 37, 243, 289}},
    {74, 9, 109, {1, 1, 5, 11, 17, 53, 117, 183, 491}},
    {75, 9, 122, {1, 1, 1, 5, 1, 13, 13, 209, 345}},
    {76, 9, 124, {1, 1, 3, 15, 1, 57, 115, 7, 33}},
    {77, 9, 137, {1, 3, 1, 11, 7, 43, 81, 207, 175}},
    {78, 9, 138, {1, 3, 1, 1, 15, 27, 63, 255, 49}},
    {79, 9, 143, {1, 3, 5, 3, 27, 61, 105, 171, 305}},
    {80, 9, 145, {1, 1, 5, 3, 1, 3, 57, 249, 149}},
    {81, 9, 152, {1, 1, 3, 5, 5, 57, 15, 13, 159}},
    {82, 9, 157, {1, 1, 1, 11, 7, 11, 105, 141, 225}},
    {83, 9, 167, {1, 3, 3, 5, 27, 59, 121, 101, 271}},
    {84, 9, 173, {1, 3, 5, 9, 11, 49, 51, 59, 115}},
    {85, 9, 176, {1, 1, 7, 1, 23, 45, 125, 71, 419}},
    {86, 9, 181, {1, 1, 3, 5, 23, 5, 105, 109, 75}},
    {87, 9, 182, {1, 1, 7, 15, 7, 11, 67, 121, 453}},
    {88, 9, 185, {1, 3, 7, 3, 9, 13, 31, 27, 449}},
    {89, 9, 191, {1, 3, 1, 15, 19, 39, 39, 89, 15}},
    {90, 9, 194, {1, 1, 1, 1, 1, 33, 73, 145, 379}},
    {91, 9, 199, {1, 3, 1, 15, 15, 43, 29, 13, 483}},
    {92, 9, 218, {1, 1, 7, 3, 19, 27, 85, 131, 431}},
    {93, 9, 220, {1, 3, 3, 3, 5, 35, 23, 195, 349}},
    {94, 9, 227, {1, 3, 3, 7, 9, 27, 39, 59, 297}},
    {95, 9, 229, {1, 1, 3, 9, 11, 17, 13, 241, 157}},
    {96, 9, 230, {1, 3, 7, 15, 25, 57, 33, 189, 213}},
    {97, 9, 234, {1, 1, 7, 1, 9, 55, 73, 83, 217}},
    {98, 9, 236, {1, 3, 3, 13, 19, 27, 23, 113, 249}},
    {99, 9, 241, {1, 3, 5, 3, 23, 43, 3, 253, 479}},
    {100, 9, 244, {1, 1, 5, 5, 11, 5, 45, 117, 217}},
    {101, 9, 253, {1, 3, 3, 7, 29, 37, 33, 123, 147}},
    {102, 10, 4, {1, 3, 1, 15, 5, 5, 37, 227, 223, 459}},
    {103, 10, 13, {1, 1, 7, 5, 5, 39, 63, 255, 135, 487}},
    {104, 10, 19, {1, 3, 1, 7, 9, 7, 87, 249, 217, 599}},
    {105, 10, 22, {1, 1, 3, 13, 9, 47, 7, 225, 363, 247}},
    {106, 10, 50, {1, 3, 7, 13, 19, 13, 9, 67, 9, 737}},
    {107, 10, 55, {1, 3, 5, 5, 19, 59, 7, 41, 319, 677}},
    {108, 10, 64, {1, 1, 5, 3, 31, 63, 15, 43, 207, 789}},
    {109, 10, 69, {1, 1, 7, 9, 13, 39, 3, 47, 497, 169}},
    {110, 10, 98, {1, 3, 1, 7, 21, 17, 97, 19, 415, 905}},
    {111, 10, 107, {1, 3, 7, 1, 3, 31, 71, 111, 165, 127}},
    {112, 10, 115, {1, 1, 5, 11, 1, 61, 83, 119, 203, 847}},
    {113, 10, 121, {1, 3, 3, 13, 9, 61, 19, 97, 47, 35}},
    {114, 10, 127, {1, 1, 7, 7, 15, 29, 63, 95, 417, 469}},
    {115, 10, 134, {1, 3, 1, 9, 25, 9, 71, 57, 213, 385}},
    {116, 10, 140, {1, 3, 5, 13, 31, 47, 101, 57, 39, 341}},
    {117, 10, 145, {1, 1, 3, 3, 31, 57, 125, 173, 365, 551}},
    {118, 10, 152, {1, 3, 7, 1, 13, 57, 67, 157, 451, 707}},
    {119, 10, 158, {1, 1, 1, 7, 21, 13, 105, 89, 429, 965}},
    {120, 10, 161, {1, 1, 5, 9, 17, 51, 45, 119, 157, 141}},
    {121, 10, 171, {1, 3, 7, 7, 13, 45, 91, 9, 129, 741}},
    {122, 10, 181, {1, 3, 7, 1, 23, 57, 67, 141, 151, 571}},
    {123, 10, 194, {1, 1, 3, 11, 17, 47, 93, 107, 375, 157}},
    {124, 10, 199, {1, 3, 3, 5, 11, 21, 43, 51, 169, 915}},
    {125, 10, 203, {1, 1, 5, 3, 15, 55, 101, 67, 455, 625}},
    {126, 10, 208, {1, 3, 5, 9, 1, 23, 29, 47, 345, 595}},
    {127, 10, 227, {1, 3, 7, 7, 5, 49, 29, 155, 323, 589}},
    {128, 10, 242, {1, 3, 3, 7, 5, 41, 127, 61, 261, 717}},
    {129, 10, 251, {1, 3, 7, 7, 17, 23, 117, 67, 129, 1009}},
    {130, 10, 253, {1, 1, 3, 13, 11, 39, 21, 207, 123, 305}},
    {131, 10, 265, {1, 1, 3, 9, 29, 3, 95, 47, 231, 73}},
    {132, 10, 266, {1, 3, 1, 9, 1, 29, 117, 21, 441, 259}},
    {133, 10, 274, {1, 3, 1, 13, 21, 39, 125, 211, 439, 723}},
    {134, 10, 283, {1, 1, 7, 3, 17, 63, 115, 89, 49, 773}},
    {135, 10, 289, {1, 3, 7, 13, 11, 33, 101, 107, 63, 73}},
    {136, 10, 295, {1, 1, 5, 5, 13, 57, 63, 135, 437, 177}},
    {137, 10, 301, {1, 1, 3, 7, 27, 63, 93, 47, 417, 483}},
    {138, 10, 316, {1, 1, 3, 1, 23, 29, 1, 191, 49, 23}},
    {139, 10, 319, {1, 1, 3, 15, 25, 55, 9, 101, 219, 607}},
    {140, 10, 324, {1, 3, 1, 7, 7, 19, 51, 251, 393, 307}},
    {141, 10, 346, {1, 3, 3, 3, 25, 55, 17, 75, 337, 3}},
    {142, 10, 352, {1, 1, 1, 13, 25, 17, 65, 45, 479, 413}},
    {143, 10, 361, {1, 1, 7, 7, 27, 49, 99, 161, 213, 727}},
    {144, 10, 367, {1, 3, 5, 1, 23, 5, 43, 41, 251, 857}},
    {145, 10, 382, {1, 3, 3, 7, 11, 61, 39, 87, 383, 835}},
    {146, 10, 395, {1, 1, 3, 15, 13, 7, 29, 7, 505, 923}},
    {147, 10, 398, {1, 3, 7, 1, 5, 31, 47, 157, 445, 501}},
    {148, 10, 400, {1, 1, 3, 7, 1, 43, 9, 147, 115, 605}},
    {149, 10, 412, {1, 3, 3, 13, 5, 1, 119, 211, 455, 1001}},
    {150, 10, 419, {1, 1, 3, 5, 13, 19, 3, 243, 75, 843}},
    {151, 10, 422, {1, 3, 7, 7, 1, 19, 91, 249, 357, 589}},
    {152, 10, 426, {1, 1, 1, 9, 1, 25, 109, 197, 279, 411}},
    {153, 10, 428, {1, 3, 1, 15, 23, 57, 59, 135, 191, 75}},
    {154, 10, 433, {1, 1, 5, 15, 29, 21, 39, 253, 383, 349}},
    {155, 10, 446, {1, 3, 3, 5, 19, 45, 61, 151, 199, 981}},
    {156, 10, 454, {1, 3, 5, 13, 9, 61, 107, 141, 141, 1}},
    {157, 10, 457, {1, 3, 1, 11, 27, 25, 85, 105, 309, 979}},
    {158, 10, 472, {1, 3, 3, 11, 19, 7, 115, 223, 349, 43}},
    {159, 10, 493, {1, 1, 7, 9, 21, 39, 123, 21, 275, 927}},
    {160, 10, 505, {1, 1, 7, 13, 15, 41, 47, 243, 303, 437}},
    {161, 10, 508, {1, 1, 1, 7, 7, 3, 15, 99, 409, 719}},
    {162, 11, 2, {1, 3, 3, 15, 27, 49, 113, 123, 113, 67, 469}},
    {163, 11, 11, {1, 3, 7, 11, 3, 23, 87, 169, 119, 483, 199}},
    {164, 11, 21, {1, 1, 5, 15, 7, 17, 109, 229, 179, 213, 741}},
    {165, 11, 22, {1, 1, 5, 13, 11, 17, 25, 135, 403, 557, 1433}},
    {166, 11, 35, {1, 3, 1, 1, 1, 61, 67, 215, 189, 945, 1243}},
    {167, 11, 49, {1, 1, 7, 13, 17, 33, 9, 221, 429, 217, 1679}},
    {168, 11, 50, {1, 1, 3, 11, 27, 3, 15, 93, 93, 865, 1049}},
    {169, 11, 56, {1, 3, 7, 7, 25, 41, 121, 35, 373, 379, 1547}},
    {170, 11, 61, {1, 3, 3, 9, 11, 35, 45, 205, 241, 9, 59}},
    {171, 11, 70, {1, 3, 1, 7, 3, 51, 7, 177, 53, 975, 89}},
    {172, 11, 74, {1, 1, 3, 5, 27, 1, 113, 231, 299, 759, 861}},
    {173, 11, 79, {1, 3, 3, 15, 25, 29, 5, 255, 139, 891, 2031}},
    {174, 11, 84, {1, 3, 1, 1, 13, 9, 109, 193, 419, 95, 17}},
    {175, 11, 88, {1, 1, 7, 9, 3, 7, 29, 41, 135, 839, 867}},
    {176, 11, 103, {1, 1, 7, 9, 25, 49, 123, 217, 113, 909, 215}},
    {177, 11, 104, {1, 1, 7, 3, 23, 15, 43, 133, 217, 327, 901}},
    {178, 11, 112, {1, 1, 3, 3, 13, 53, 63, 123, 477, 711, 1387}},
    {179, 11, 115, {1, 1, 3, 15, 7, 29, 75, 119, 181, 957, 247}},
    {180, 11, 117, {1, 1, 1, 11, 27, 25, 109, 151, 267, 99, 1461}},
    {181, 11, 122, {1, 3, 7, 15, 5, 5, 53, 145, 11, 725, 1501}},
    {182, 11, 134, {1, 3, 7, 1, 9, 43, 71, 229, 157, 607, 1835}},
    {183, 11, 137, {1, 3, 3, 13, 25, 1, 5, 27, 471, 349, 127}},
    {184, 11, 146, {1, 1, 1, 1, 23, 37, 9, 221, 269, 897, 1685}},
    {185, 11, 148, {1, 1, 3, 3, 31, 29, 51, 19, 311, 553, 1969}},
    {186, 11, 157, {1, 3, 7, 5, 5, 55, 17, 39, 475, 671, 1529}},
    {187, 11, 158, {1, 1, 7, 1, 1, 35, 47, 27, 437, 395, 1635}},
    {188, 11, 162, {1, 1, 7, 3, 13, 23, 43, 135, 327, 139, 389}},
    {189, 11, 164, {1, 3, 7, 3, 9, 25, 91, 25, 429, 219, 513}},
    {190, 11, 168, {1, 1, 3, 5, 13, 29, 119, 201, 277, 157, 2043}},
    {191, 11, 173, {1, 3, 5, 3, 29, 57, 13, 17, 167, 739, 1031}},
    {192, 11, 185, {1, 3, 3, 5, 29, 21, 95, 27, 255, 679, 1531}},
    {193, 11, 186, {1, 3, 7, 15, 9, 5, 21, 71, 61, 961, 1201}},
    {194, 11, 191, {1, 3, 5, 13, 15, 57, 33, 93, 459, 867, 223}},
    {195, 11, 193, {1, 1, 1, 15, 17, 43, 127, 191, 67, 177, 1073}},
    {196, 11, 199, {1, 1, 1, 15, 23, 7, 21, 199, 75, 293, 1611}},
    {197, 11, 213, {1, 3, 7, 13, 15, 39, 21, 149, 65, 741, 319}},
    {198, 11, 214, {1, 3, 7, 11, 23, 13, 101, 89, 277, 519, 711}},
    {199, 11, 220, {1, 3, 7, 15, 19, 27, 85, 203, 441, 97, 1895}},
    {200, 11, 227, {1, 3, 1, 3, 29, 25, 21, 155, 11, 191, 197}},
    {201, 11, 236, {1, 1, 7, 5, 27, 11, 81, 101, 457, 675, 1687}},
    {202, 11, 242, {1, 3, 1, 5, 25, 5, 65, 193, 41, 567, 781}},
    {203, 11, 251, {1, 3, 1, 5, 11, 15, 113, 77, 411, 695, 1111}},
    {204, 11, 256, {1, 1, 3, 9, 11, 53, 119, 171, 55, 297, 509}},
    {205, 11, 259, {1, 1, 1, 1, 11, 39, 113, 139, 165, 347, 595}},
    {206, 11, 265, {1, 3, 7, 11, 9, 17, 101, 13, 81, 325, 1733}},
    {207, 11, 266, {1, 3, 1, 1, 21, 43, 115, 9, 113, 907, 645}},
    {208, 11, 276, {1, 1, 7, 3, 9, 25, 117, 197, 159, 471, 475}},
    {209, 11, 292, {1, 3, 1, 9, 11, 21, 57, 207, 485, 613, 1661}},
    {210, 11, 304, {1, 1, 7, 7, 27, 55, 49, 223, 89, 85, 1523}},
    {211, 11, 310, {1, 1, 5, 3, 19, 41, 45, 51, 447, 299, 1355}},
    {212, 11, 316, {1, 3, 1, 15, 1, 35, 119, 135, 427, 93, 1311}},
    {213, 11, 319, {1, 3, 1, 15, 31, 39, 121, 145, 129, 903, 333}},
    {214, 11, 322, {1, 1, 5, 3, 29, 7, 9, 11, 395, 119, 873}},
    {215, 11, 328, {1, 3, 5, 11, 27, 29, 5, 117, 469, 31, 1811}},
    {216, 11, 334, {1, 1, 7, 15, 21, 25, 71, 15, 89, 1021, 679}},
    {217, 11, 339, {1, 3, 7, 9, 21, 39, 51, 111, 327, 809, 845}},
    {218, 11, 341, {1, 3, 3, 13, 3, 33, 79, 17, 183, 599, 1859}},
    {219, 11, 345, {1, 1, 7, 9, 31, 9, 1, 5, 353, 395, 833}},
    {220, 11, 346, {1, 3, 5, 7, 3, 53, 81, 133, 155, 355, 1559}},
    {221, 11, 362, {1, 3, 5, 5, 31, 13, 89, 195, 357, 769, 889}},
    {222, 11, 367, {1, 1, 7, 1, 9, 21, 77, 31, 269, 857, 923}},
    {223, 11, 372, {1, 1, 1, 11, 11, 27, 61, 185, 329, 685, 325}},
    {224, 11, 375, {1, 1, 1, 5, 11, 31, 71, 79, 293, 29, 17}},
    {225, 11, 376, {1, 1, 7, 7, 7, 41, 65, 167, 67, 153, 1305}},
    {226, 11, 381, {1, 3, 3, 5, 23, 45, 109, 205, 191, 649, 749}},
    {227, 11, 385, {1, 1, 7, 7, 17, 1, 73, 211, 19, 797, 1009}},
    {228, 11, 388, {1, 1, 5, 9, 23, 15, 117, 213, 183, 477, 1301}},
    {229, 11, 392, {1, 1, 5, 13, 23, 35, 55, 151, 267, 883, 1479}},
    {230, 11, 409, {1, 1, 1, 7, 5, 43, 77, 11, 149, 297, 329}},
    {231, 11, 415, {1, 1, 7, 15, 3, 41, 55, 123, 219, 499, 377}},
    {232, 11, 416, {1, 3, 3, 1, 27, 7, 113, 141, 173, 379, 1087}},
    {233, 11, 421, {1, 3, 1, 9, 7, 25, 45, 49, 415, 329, 483}},
    {234, 11, 428, {1, 1, 7, 7, 7, 15, 75, 191, 305, 757, 813}},
    {235, 11, 431, {1, 3, 7, 5, 31, 15, 21, 247, 29, 297, 1015}},
    {236, 11, 434, {1, 3, 1, 13, 3, 41, 69, 235, 431, 515, 1889}},
    {237, 11, 439, {1, 1, 5, 7, 31, 5, 69, 193, 229, 439, 1043}},
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    {828, 13, 2276, {1, 1, 7, 3, 21, 21, 97, 73, 73, 147, 1905, 2391, 3743}},
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    {836, 13, 2311, {1, 3, 5, 1, 3, 21, 89, 27, 171, 121, 1453, 3273, 2891}},
    {837, 13, 2318, {1, 3, 5, 5, 29, 19, 79, 77, 343, 969, 1759, 1921, 4189}},
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    {841, 13, 2345, {1, 1, 3, 1, 13, 43, 107, 189, 475, 679, 1843, 33, 6895}},
    {842, 13, 2348, {1, 3, 5, 9, 17, 13, 107, 245, 415, 531, 265, 3165, 3189}},
    {843, 13, 2354, {1, 3, 1, 3, 31, 29, 103, 233, 31, 445, 649, 3377, 3207}},
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    {845, 13, 2377, {1, 1, 3, 3, 21, 19, 113, 35, 173, 871, 275, 1901, 6725}},
    {846, 13, 2380, {1, 1, 3, 7, 27, 45, 41, 93, 463, 209, 1721, 1863, 7893}},
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    {849, 13, 2395, {1, 1, 1, 15, 29, 43, 13, 241, 403, 349, 685, 987, 4177}},
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    {852, 13, 2411, {1, 1, 3, 7, 21, 35, 101, 131, 129, 757, 199, 1881, 737}},
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    {854, 13, 2419, {1, 1, 3, 9, 11, 43, 7, 159, 25, 725, 1169, 1757, 3499}},
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    {856, 13, 2442, {1, 3, 3, 15, 19, 41, 75, 163, 51, 511, 1785, 4033, 7791}},
    {857, 13, 2455, {1, 3, 7, 15, 29, 45, 81, 189, 401, 71, 1597, 3671, 2133}},
    {858, 13, 2472, {1, 1, 3, 1, 3, 17, 119, 55, 217, 485, 1217, 1475, 5791}},
    {859, 13, 2478, {1, 1, 7, 9, 21, 61, 71, 175, 205, 413, 1645, 2375, 89}},
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    {862, 13, 2509, {1, 1, 1, 7, 1, 61, 75, 131, 65, 891, 349, 2767, 3855}},
    {863, 13, 2517, {1, 3, 5, 9, 29, 57, 61, 79, 303, 997, 1053, 1973, 1547}},
    {864, 13, 2524, {1, 1, 3, 7, 19, 9, 57, 197, 253, 597, 1971, 1831, 8097}},
    {865, 13, 2528, {1, 3, 1, 9, 3, 13, 29, 169, 25, 957, 1575, 2955, 3549}},
    {866, 13, 2531, {1, 1, 5, 11, 17, 37, 79, 91, 11, 687, 1511, 1065, 1539}},
    {867, 13, 2538, {1, 1, 1, 7, 1, 59, 1, 49, 23, 73, 881, 1661, 3841}},
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    {871, 13, 2557, {1, 3, 1, 5, 13, 55, 101, 89, 239, 907, 1559, 1421, 87}},
    {872, 13, 2564, {1, 1, 3, 9, 23, 27, 41, 189, 35, 155, 683, 2491, 7495}},
    {873, 13, 2573, {1, 3, 5, 3, 5, 47, 39, 161, 279, 945, 365, 15, 4643}},
    {874, 13, 2579, {1, 1, 1, 11, 21, 7, 125, 195, 23, 635, 1949, 2237, 1885}},
    {875, 13, 2592, {1, 1, 3, 7, 13, 25, 105, 145, 203, 701, 1525, 1391, 1637}},
    {876, 13, 2598, {1, 3, 3, 13, 7, 43, 13, 39, 301, 507, 405, 2333, 2405}},
    {877, 13, 2607, {1, 1, 5, 15, 25, 19, 31, 67, 81, 781, 1541, 3743, 2787}},
    {878, 13, 2612, {1, 1, 1, 11, 15, 7, 87, 129, 151, 225, 655, 1569, 5299}},
    {879, 13, 2619, {1, 1, 5, 3, 3, 33, 97, 255, 9, 667, 787, 3557, 5273}},
    {880, 13, 2621, {1, 1, 3, 3, 1, 7, 13, 31, 31, 1021, 1863, 2897, 6389}},
    {881, 13, 2627, {1, 3, 1, 15, 13, 29, 93, 27, 229, 599, 521, 1631, 3683}},
    {882, 13, 2633, {1, 1, 7, 9, 11, 27, 43, 95, 149, 159, 495, 2711, 2189}},
    {883, 13, 2636, {1, 1, 7, 9, 11, 51, 43, 121, 299, 73, 1991, 561, 6781}},
    {884, 13, 2642, {1, 1, 3, 3, 7, 61, 125, 13, 415, 11, 15, 2463, 385}},
    {885, 13, 2654, {1, 3, 5, 1, 27, 23, 1, 47, 149, 371, 1599, 341, 1595}},
    {886, 13, 2660, {1, 1, 1, 15, 3, 39, 65, 5, 33, 713, 399, 2935, 3825}},
    {887, 13, 2669, {1, 1, 7, 7, 17, 39, 3, 235, 227, 231, 323, 2869, 4747}},
    {888, 13, 2675, {1, 1, 5, 9, 13, 11, 41, 155, 393, 701, 909, 2999, 5053}},
    {889, 13, 2684, {1, 1, 3, 7, 5, 41, 105, 13, 123, 429, 1455, 2501, 1065}},
    {890, 13, 2694, {1, 1, 1, 7, 17, 21, 95, 141, 305, 951, 1305, 3639, 3797}},
    {891, 13, 2703, {1, 3, 5, 9, 7, 59, 29, 129, 265, 889, 993, 1411, 2069}},
    {892, 13, 2706, {1, 1, 1, 11, 3, 51, 9, 35, 355, 131, 1307, 1547, 701}},
    {893, 13, 2712, {1, 1, 7, 3, 17, 57, 113, 197, 483, 831, 1741, 3897, 3649}},
    {894, 13, 2715, {1, 1, 5, 11, 1, 33, 7, 243, 95, 905, 1933, 2123, 7381}},
    {895, 13, 2722, {1, 3, 3, 15, 5, 37, 1, 235, 77, 375, 1231, 1029, 1839}},
    {896, 13, 2727, {1, 1, 5, 3, 31, 11, 103, 245, 373, 103, 25, 1283, 6155}},
    {897, 13, 2734, {1, 3, 5, 1, 25, 25, 51, 159, 381, 97, 799, 565, 5165}},
    {898, 13, 2742, {1, 1, 7, 13, 25, 21, 109, 3, 253, 459, 623, 2817, 7815}},
    {899, 13, 2745, {1, 3, 5, 1, 23, 5, 127, 157, 187, 187, 1383, 2777, 2413}},
    {900, 13, 2751, {1, 1, 5, 3, 29, 47, 97, 197, 215, 725, 445, 2111, 1701}},
    {901, 13, 2766, {1, 3, 1, 9, 27, 25, 105, 59, 333, 79, 1099, 3695, 5725}},
    {902, 13, 2768, {1, 1, 7, 3, 11, 15, 127, 151, 163, 967, 665, 733, 509}},
    {903, 13, 2780, {1, 3, 3, 3, 15, 5, 51, 17, 409, 679, 229, 1037, 353}},
    {904, 13, 2790, {1, 3, 7, 15, 7, 9, 17, 115, 205, 105, 597, 2913, 1941}},
    {905, 13, 2794, {1, 1, 5, 11, 31, 1, 99, 213, 33, 319, 617, 1493, 7287}},
    {906, 13, 2796, {1, 3, 5, 5, 21, 31, 115, 43, 309, 217, 1, 3363, 6673}},
    {907, 13, 2801, {1, 3, 7, 7, 11, 29, 125, 75, 209, 217, 1749, 1565, 4431}},
    {908, 13, 2804, {1, 3, 5, 1, 5, 37, 103, 237, 19, 763, 915, 753, 7479}},
    {909, 13, 2807, {1, 3, 3, 9, 11, 59, 9, 133, 455, 683, 251, 963, 3743}},
    {910, 13, 2816, {1, 3, 5, 9, 7, 41, 97, 185, 117, 367, 2045, 3013, 6249}},
    {911, 13, 2821, {1, 1, 1, 5, 29, 51, 53, 147, 379, 769, 865, 2273, 1755}},
    {912, 13, 2831, {1, 3, 1, 7, 13, 61, 125, 153, 297, 385, 1981, 2221, 4209}},
    {913, 13, 2834, {1, 1, 7, 15, 7, 33, 41, 43, 201, 819, 129, 757, 4087}},
    {914, 13, 2839, {1, 1, 5, 7, 31, 15, 19, 15, 197, 921, 1967, 491, 4911}},
    {915, 13, 2845, {1, 1, 1, 13, 21, 25, 119, 123, 255, 155, 1765, 2895, 4201}},
    {916, 13, 2852, {1, 3, 5, 9, 1, 63, 57, 193, 327, 455, 1729, 1259, 7483}},
    {917, 13, 2856, {1, 3, 5, 1, 5, 19, 71, 255, 257, 477, 1799, 3855, 955}},
    {918, 13, 2861, {1, 1, 3, 1, 29, 27, 7, 151, 327, 311, 235, 3599, 6165}},
    {919, 13, 2873, {1, 3, 3, 3, 7, 29, 113, 87, 339, 271, 1141, 1111, 7971}},
    {920, 13, 2874, {1, 3, 5, 15, 23, 51, 57, 233, 179, 397, 1059, 123, 697}},
    {921, 13, 2888, {1, 3, 3, 13, 17, 11, 15, 189, 437, 449, 1533, 2209, 1849}},
    {922, 13, 2893, {1, 3, 5, 9, 9, 19, 53, 165, 279, 875, 1223, 1585, 6647}},
    {923, 13, 2894, {1, 1, 7, 5, 5, 49, 119, 31, 273, 919, 413, 1531, 6233}},
    {924, 13, 2902, {1, 3, 5, 5, 1, 19, 27, 213, 413, 271, 223, 299, 5635}},
    {925, 13, 2917, {1, 1, 7, 3, 11, 55, 25, 43, 147, 53, 95, 1849, 7701}},
    {926, 13, 2921, {1, 3, 5, 11, 17, 35, 9, 3, 117, 729, 21, 3379, 5963}},
    {927, 13, 2922, {1, 3, 1, 7, 23, 25, 45, 103, 181, 677, 1155, 205, 1967}},
    {928, 13, 2929, {1, 1, 3, 9, 19, 53, 41, 243, 97, 199, 407, 3299, 5309}},
    {929, 13, 2935, {1, 3, 5, 11, 27, 27, 59, 153, 501, 855, 1235, 2295, 5535}},
    {930, 13, 2946, {1, 1, 3, 7, 11, 37, 1, 179, 289, 895, 511, 697, 5067}},
    {931, 13, 2951, {1, 3, 7, 15, 25, 27, 33, 37, 351, 351, 813, 2239, 1561}},
    {932, 13, 2957, {1, 3, 1, 7, 25, 51, 79, 65, 427, 293, 1031, 685, 533}},
    {933, 13, 2960, {1, 3, 3, 15, 21, 21, 77, 31, 299, 643, 161, 2991, 7911}},
    {934, 13, 2966, {1, 3, 3, 7, 7, 61, 99, 19, 43, 35, 687, 1449, 5211}},
    {935, 13, 2972, {1, 3, 1, 5, 5, 59, 101, 175, 149, 799, 439, 19, 7565}},
    {936, 13, 2976, {1, 3, 7, 9, 31, 13, 75, 227, 337, 207, 609, 2119, 3539}},
    {937, 13, 2979, {1, 1, 1, 11, 3, 59, 1, 139, 425, 583, 263, 2687, 4445}},
    {938, 13, 2985, {1, 1, 5, 7, 21, 31, 55, 117, 377, 469, 1907, 3091, 3221}},
    {939, 13, 3000, {1, 1, 5, 1, 7, 63, 89, 197, 271, 425, 1493, 2337, 6397}},
    {940, 13, 3003, {1, 1, 1, 7, 9, 35, 17, 237, 215, 211, 523, 3095, 1771}},
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    {947, 13, 3048, {1, 1, 7, 11, 31, 41, 17, 3, 163, 207, 407, 1475, 5911}},
    {948, 13, 3051, {1, 1, 7, 3, 3, 19, 87, 199, 77, 207, 1957, 1691, 5045}},
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    {953, 13, 3074, {1, 3, 5, 9, 19, 51, 25, 39, 7, 973, 837, 105, 1987}},
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    {957, 13, 3097, {1, 3, 7, 15, 9, 27, 61, 85, 81, 371, 1803, 3683, 4771}},
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    {960, 13, 3124, {1, 3, 1, 5, 7, 53, 53, 121, 299, 633, 263, 3651, 3187}},
    {961, 13, 3128, {1, 3, 1, 9, 31, 59, 73, 5, 475, 763, 115, 2263, 2475}},
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    {963, 13, 3160, {1, 3, 5, 3, 17, 7, 29, 93, 253, 527, 657, 1859, 763}},
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    {965, 13, 3172, {1, 1, 3, 11, 1, 37, 65, 135, 345, 307, 305, 1167, 1767}},
    {966, 13, 3175, {1, 3, 3, 13, 5, 33, 9, 245, 271, 123, 1865, 2215, 2791}},
    {967, 13, 3184, {1, 1, 3, 1, 9, 23, 3, 21, 149, 923, 1335, 1015, 45}},
    {968, 13, 3193, {1, 3, 1, 15, 11, 3, 65, 219, 233, 353, 771, 3961, 1515}},
    {969, 13, 3196, {1, 3, 1, 5, 15, 41, 87, 141, 19, 905, 449, 3727, 1875}},
    {970, 13, 3200, {1, 1, 7, 9, 11, 15, 53, 151, 243, 279, 1695, 2317, 6661}},
    {971, 13, 3203, {1, 3, 3, 7, 19, 51, 31, 157, 79, 399, 465, 661, 1029}},
    {972, 13, 3205, {1, 3, 5, 1, 5, 41, 3, 33, 157, 385, 1943, 1851, 3121}},
    {973, 13, 3209, {1, 3, 1, 11, 25, 59, 105, 191, 151, 285, 801, 201, 6871}},
    {974, 13, 3224, {1, 3, 1, 15, 27, 35, 17, 195, 387, 907, 1905, 2177, 2597}},
    {975, 13, 3239, {1, 3, 1, 9, 31, 43, 71, 185, 469, 809, 541, 571, 107}},
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    {977, 13, 3254, {1, 1, 3, 15, 19, 59, 45, 147, 165, 223, 259, 1205, 431}},
    {978, 13, 3265, {1, 1, 5, 13, 5, 53, 115, 57, 203, 151, 1039, 871, 3881}},
    {979, 13, 3266, {1, 3, 5, 15, 1, 29, 115, 249, 79, 957, 143, 3425, 5769}},
    {980, 13, 3275, {1, 1, 7, 15, 15, 15, 117, 181, 363, 17, 1871, 1049, 2997}},
    {981, 13, 3280, {1, 1, 3, 7, 23, 11, 77, 123, 149, 1019, 93, 3637, 6975}},
    {982, 13, 3283, {1, 1, 1, 7, 5, 51, 77, 89, 121, 155, 1839, 1301, 2771}},
    {983, 13, 3286, {1, 3, 7, 7, 7, 39, 33, 69, 169, 535, 1699, 2117, 3233}},
    {984, 13, 3301, {1, 3, 5, 7, 3, 59, 81, 113, 261, 627, 79, 227, 7623}},
    {985, 13, 3302, {1, 3, 5, 5, 13, 57, 121, 41, 11, 111, 1055, 3313, 3371}},
    {986, 13, 3305, {1, 1, 3, 13, 13, 9, 47, 197, 303, 987, 1125, 2461, 5007}},
    {987, 13, 3319, {1, 3, 1, 5, 1, 59, 109, 49, 453, 673, 2017, 205, 4673}},
    {988, 13, 3323, {1, 3, 1, 13, 19, 43, 95, 247, 475, 193, 1513, 885, 5391}},
    {989, 13, 3326, {1, 1, 1, 11, 29, 57, 77, 101, 433, 537, 1681, 2463, 6623}},
    {990, 13, 3331, {1, 3, 7, 13, 3, 61, 29, 53, 29, 673, 1037, 3877, 7421}},
    {991, 13, 3348, {1, 3, 3, 11, 5, 59, 61, 91, 13, 949, 1093, 1291, 7395}},
    {992, 13, 3351, {1, 3, 3, 13, 21, 27, 49, 37, 429, 877, 1247, 2375, 737}},
    {993, 13, 3358, {1, 3, 5, 3, 25, 19, 75, 187, 239, 971, 859, 2519, 7323}},
    {994, 13, 3368, {1, 3, 3, 7, 25, 19, 11, 223, 75, 801, 313, 2875, 6857}},
    {995, 13, 3374, {1, 1, 7, 3, 13, 63, 49, 125, 65, 1005, 1757, 3685, 4385}},
    {996, 13, 3376, {1, 3, 1, 15, 5, 41, 95, 231, 505, 907, 751, 3207, 4115}},
    {997, 13, 3379, {1, 1, 7, 11, 31, 7, 29, 51, 449, 151, 1821, 3317, 931}},
    {998, 13, 3385, {1, 3, 1, 11, 19, 11, 19, 47, 111, 637, 37, 3707, 2599}},
    {999, 13, 3386, {1, 3, 7, 5, 23, 27, 65, 217, 491, 129, 1715, 2479, 2015}},
    {1000, 13, 3396, {1, 1, 5, 3, 5, 51, 43, 253, 495, 105, 1183, 3409, 1469}},
    {1001, 13, 3420, {1, 3, 7, 9, 21, 5, 87, 67, 481, 405, 1967, 2837, 5161}},
    {1002, 13, 3423, {1, 1, 7, 3, 29, 25, 15, 211, 233, 301, 1037, 3853, 7115}},
    {1003, 13, 3430, {1, 3, 5, 9, 3, 15, 85, 81, 141, 395, 845, 17, 7485}},
    {1004, 13, 3433, {1, 3, 5, 3, 21, 37, 39, 93, 461, 615, 1725, 1745, 5137}},
    {1005, 13, 3434, {1, 1, 3, 1, 1, 21, 21, 207, 271, 447, 1415, 2507, 3291}},
    {1006, 13, 3439, {1, 3, 7, 11, 23, 3, 115, 191, 257, 1015, 463, 1501, 7439}},
    {1007, 13, 3442, {1, 1, 7, 11, 3, 53, 101, 221, 9, 225, 1799, 1701, 5669}},
    {1008, 13, 3444, {1, 1, 7, 13, 17, 27, 7, 115, 67, 645, 1283, 75, 1881}},
    {1009, 13, 3453, {1, 1, 3, 15, 7, 39, 75, 85, 127, 379, 1509, 2215, 5697}},
    {1010, 13, 3464, {1, 1, 7, 1, 19, 31, 11, 67, 263, 877, 337, 1655, 1855}},
    {1011, 13, 3477, {1, 3, 5, 9, 11, 47, 125, 89, 235, 331, 159, 685, 999}},
    {1012, 13, 3478, {1, 3, 7, 3, 23, 39, 59, 69, 221, 291, 725, 2831, 4743}},
    {1013, 13, 3482, {1, 3, 7, 11, 1, 43, 127, 235, 143, 329, 1823, 21, 73}},
    {1014, 13, 3487, {1, 3, 1, 3, 27, 23, 33, 29, 493, 775, 1873, 1005, 2869}},
    {1015, 13, 3497, {1, 3, 3, 9, 3, 31, 63, 249, 353, 849, 5, 2787, 4759}},
    {1016, 13, 3500, {1, 3, 3, 11, 15, 15, 73, 159, 433, 35, 1203, 2541, 6713}},
    {1017, 13, 3505, {1, 1, 5, 1, 13, 17, 107, 101, 411, 861, 1075, 2161, 3923}},
    {1018, 13, 3506, {1, 1, 3, 5, 29, 29, 55, 205, 235, 685, 1445, 2413, 6837}},
    {1019, 13, 3511, {1, 1, 1, 13, 13, 1, 125, 37, 331, 33, 47, 2761, 3449}},
    {1020, 13, 3512, {1, 1, 7, 3, 17, 21, 21, 93, 145, 423, 1057, 997, 6117}},
    {1021, 13, 3515, {1, 3, 3, 13, 25, 47, 13, 159, 41, 907, 1543, 1919, 5547}},
    {1022, 13, 3525, {1, 1, 3, 9, 29, 53, 83, 45, 133, 453, 183, 2939, 4945}},
    {1023, 13, 3532, {1, 1, 1, 7, 9, 7, 89, 71, 315, 983, 1471, 2475, 7077}},
    {1024, 13, 3538, {1, 1, 3, 3, 31, 21, 55, 37, 337, 63, 299, 2415, 153}},
    {1025, 13, 3540, {1, 1, 7, 3, 27, 59, 85, 109, 405, 337, 393, 2291, 5423}},
    {1026, 13, 3547, {1, 1, 1, 1, 5, 31, 33, 43, 141, 9, 1271, 1749, 6281}},
    {1027, 13, 3549, {1, 1, 3, 9, 23, 35, 25, 17, 49, 119, 883, 2907, 3573}},
    {1028, 13, 3560, {1, 3, 1, 15, 25, 61, 89, 15, 315, 1015, 563, 1895, 4123}},
    {1029, 13, 3571, {1, 3, 3, 7, 15, 53, 61, 225, 381, 217, 163, 4005, 7269}},
    {1030, 13, 3577, {1, 3, 7, 5, 1, 59, 13, 201, 53, 629, 1917, 3105, 3047}},
    {1031, 13, 3583, {1, 3, 1, 1, 19, 45, 71, 11, 15, 365, 1223, 3861, 5005}},
    {1032, 13, 3590, {1, 1, 5, 11, 15, 15, 31, 245, 105, 609, 1051, 1911, 7531}},
    {1033, 13, 3593, {1, 3, 7, 11, 27, 5, 79, 31, 201, 347, 1295, 2589, 5179}},
    {1034, 13, 3594, {1, 1, 3, 1, 31, 23, 65, 203, 359, 591, 1459, 1941, 2307}},
    {1035, 13, 3599, {1, 1, 5, 5, 3, 55, 79, 179, 147, 223, 1011, 1437, 3715}},
    {1036, 13, 3601, {1, 1, 5, 11, 23, 19, 57, 241, 363, 729, 1647, 2395, 3237}},
    {1037, 13, 3602, {1, 3, 7, 7, 7, 63, 115, 53, 485, 965, 551, 3945, 1535}},
    {1038, 13, 3613, {1, 1, 1, 15, 5, 61, 33, 213, 451, 363, 95, 1185, 3633}},
    {1039, 13, 3623, {1, 3, 5, 1, 17, 49, 39, 159, 327, 1021, 289, 3375, 8055}},
    {1040, 13, 3630, {1, 3, 3, 5, 11, 1, 73, 3, 121, 561, 209, 1913, 4549}},
    {1041, 13, 3638, {1, 3, 1, 3, 23, 39, 101, 231, 317, 397, 693, 1579, 3585}},
    {1042, 13, 3649, {1, 1, 1, 1, 1, 5, 81, 209, 373, 689, 259, 3167, 1665}},
    {1043, 13, 3655, {1, 1, 1, 11, 21, 19, 83, 201, 7, 573, 1563, 1649, 5827}},
    {1044, 13, 3662, {1, 3, 5, 1, 31, 35, 53, 149, 185, 925, 701, 3727, 4425}},
    {1045, 13, 3667, {1, 1, 5, 7, 19, 11, 67, 47, 19, 789, 1855, 293, 7569}},
    {1046, 13, 3669, {1, 1, 5, 13, 25, 55, 25, 187, 405, 1013, 493, 1645, 6753}},
    {1047, 13, 3676, {1, 1, 3, 11, 13, 23, 35, 219, 247, 723, 1079, 1523, 7383}},
    {1048, 13, 3683, {1, 1, 3, 13, 5, 1, 27, 151, 61, 889, 1911, 3859, 4661}},
    {1049, 13, 3700, {1, 3, 1, 7, 15, 59, 57, 157, 333, 367, 245, 3043, 1683}},
    {1050, 13, 3709, {1, 3, 7, 11, 15, 53, 107, 81, 287, 637, 557, 315, 4361}},
    {1051, 13, 3710, {1, 1, 5, 11, 11, 21, 35, 59, 429, 459, 1439, 639, 6907}},
    {1052, 13, 3713, {1, 3, 3, 11, 13, 51, 101, 121, 437, 9, 889, 1907, 5217}},
    {1053, 13, 3723, {1, 1, 7, 13, 7, 5, 99, 161, 207, 237, 1547, 403, 2269}},
    {1054, 13, 3725, {1, 1, 5, 9, 23, 17, 43, 113, 119, 213, 977, 1197, 1039}},
    {1055, 13, 3728, {1, 3, 3, 9, 25, 51, 79, 5, 355, 279, 875, 1947, 1261}},
    {1056, 13, 3734, {1, 1, 7, 3, 5, 15, 85, 137, 361, 509, 959, 3227, 3755}},
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    {1945, 15, 687, {1, 3, 1, 5, 7, 37, 83, 115, 199, 125, 509, 2535, 7441, 8157, 8921}},
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    {1947, 15, 701, {1, 1, 3, 3, 11, 1, 103, 93, 153, 277, 1705, 1403, 2877, 741, 22913}},
    {1948, 15, 704, {1, 3, 7, 3, 3, 47, 35, 251, 309, 323, 1159, 895, 3407, 6507, 4677}},
    {1949, 15, 710, {1, 3, 7, 15, 11, 13, 45, 51, 53, 833, 137, 1409, 7043, 4067, 13939}},
    {1950, 15, 721, {1, 1, 3, 11, 21, 39, 71, 25, 197, 645, 501, 3119, 1053, 7855, 30873}},
    {1951, 15, 728, {1, 3, 5, 15, 29, 51, 93, 31, 387, 785, 167, 3815, 5477, 4255, 17975}},
    {1952, 15, 738, {1, 1, 1, 3, 1, 33, 93, 9, 49, 389, 2009, 4095, 6299, 4451, 18043}},
    {1953, 15, 740, {1, 3, 5, 15, 13, 43, 43, 167, 361, 445, 1685, 3677, 3901, 5693, 18901}},
    {1954, 15, 749, {1, 1, 3, 9, 1, 11, 55, 61, 65, 515, 1723, 1235, 1613, 15083, 9529}},
    {1955, 15, 758, {1, 1, 3, 5, 31, 23, 107, 169, 109, 1005, 195, 3509, 4879, 15767, 23089}},
    {1956, 15, 761, {1, 3, 7, 11, 3, 35, 61, 117, 99, 311, 1909, 2329, 3499, 8701, 27507}},
    {1957, 15, 772, {1, 3, 7, 11, 1, 21, 27, 167, 77, 469, 2045, 873, 3441, 7377, 6225}},
    {1958, 15, 776, {1, 1, 5, 3, 19, 17, 97, 55, 43, 17, 577, 765, 4027, 9511, 28643}},
    {1959, 15, 782, {1, 3, 5, 7, 31, 47, 71, 41, 109, 441, 815, 1483, 6881, 595, 7263}},
    {1960, 15, 789, {1, 1, 3, 9, 21, 63, 109, 231, 303, 381, 1701, 2877, 6899, 967, 30047}},
    {1961, 15, 810, {1, 3, 5, 1, 19, 31, 21, 201, 167, 649, 823, 715, 2289, 5081, 14869}},
    {1962, 15, 812, {1, 1, 7, 13, 23, 23, 59, 217, 263, 213, 1495, 2915, 2237, 1669, 14415}},
    {1963, 15, 818, {1, 1, 3, 7, 29, 53, 109, 57, 429, 55, 573, 3529, 7687, 13853, 27299}},
    {1964, 15, 830, {1, 3, 5, 3, 23, 13, 107, 99, 81, 483, 411, 223, 2907, 5095, 28383}},
    {1965, 15, 832, {1, 1, 1, 5, 25, 29, 125, 233, 107, 381, 291, 3781, 1127, 5987, 11707}},
    {1966, 15, 852, {1, 3, 7, 13, 29, 49, 17, 209, 379, 89, 1939, 1981, 129, 10907, 21123}},
    {1967, 15, 855, {1, 3, 5, 15, 25, 37, 93, 81, 359, 675, 2039, 685, 2405, 6439, 22425}},
    {1968, 15, 859, {1, 3, 3, 7, 3, 25, 43, 179, 233, 167, 1969, 537, 2781, 9605, 2411}},
    {1969, 15, 865, {1, 3, 7, 13, 9, 49, 81, 195, 213, 593, 163, 707, 3887, 4557, 1051}},
    {1970, 15, 877, {1, 3, 5, 13, 3, 47, 5, 197, 341, 1015, 1699, 35, 6907, 11365, 15213}},
    {1971, 15, 895, {1, 3, 3, 11, 27, 13, 109, 127, 13, 895, 687, 2719, 7805, 1939, 16615}},
    {1972, 15, 901, {1, 3, 7, 11, 11, 63, 35, 131, 269, 419, 1531, 535, 87, 1667, 2889}},
    {1973, 15, 902, {1, 3, 7, 15, 31, 51, 13, 75, 411, 943, 1753, 797, 5287, 10133, 19235}},
    {1974, 15, 906, {1, 3, 5, 15, 7, 37, 113, 169, 103, 305, 1059, 1769, 4801, 1743, 25455}},
    {1975, 15, 916, {1, 1, 3, 5, 1, 33, 53, 203, 247, 697, 851, 3927, 6737, 5455, 1709}},
    {1976, 15, 920, {1, 1, 7, 9, 7, 5, 9, 201, 321, 613, 1567, 859, 3543, 2357, 11377}},
    {1977, 15, 949, {1, 1, 3, 11, 29, 11, 105, 217, 99, 971, 19, 3007, 6573, 3381, 22739}},
    {1978, 15, 962, {1, 3, 5, 1, 1, 11, 83, 215, 15, 217, 731, 873, 1275, 11457, 26937}},
    {1979, 15, 964, {1, 1, 7, 15, 19, 29, 11, 235, 193, 713, 629, 1205, 6655, 1669, 3465}},
    {1980, 15, 967, {1, 1, 7, 1, 13, 49, 89, 73, 39, 45, 301, 3723, 4603, 12853, 13695}},
    {1981, 15, 981, {1, 3, 3, 11, 27, 1, 51, 223, 495, 153, 835, 3565, 465, 9497, 8303}},
    {1982, 15, 982, {1, 1, 1, 5, 11, 25, 7, 99, 141, 247, 1335, 2307, 4639, 375, 16841}},
    {1983, 15, 985, {1, 1, 7, 11, 21, 11, 81, 123, 485, 363, 217, 2165, 4819, 11045, 9853}},
    {1984, 15, 991, {1, 3, 5, 7, 15, 43, 17, 19, 377, 601, 849, 1157, 7821, 5623, 29901}},
    {1985, 15, 1007, {1, 3, 3, 13, 15, 29, 93, 87, 445, 565, 561, 4025, 79, 12369, 30383}},
    {1986, 15, 1016, {1, 1, 3, 11, 11, 13, 31, 239, 485, 417, 1785, 1843, 2807, 1539, 15727}},
    {1987, 15, 1024, {1, 3, 1, 9, 17, 17, 7, 109, 239, 243, 53, 575, 77, 4887, 8023}},
    {1988, 15, 1051, {1, 3, 3, 7, 29, 57, 85, 161, 155, 667, 243, 581, 6307, 1947, 7165}},
    {1989, 15, 1060, {1, 3, 5, 13, 11, 37, 83, 231, 255, 899, 1795, 3049, 7169, 11451, 31227}},
    {1990, 15, 1070, {1, 1, 3, 5, 29, 7, 19, 143, 53, 191, 1525, 2685, 1377, 6229, 25141}},
    {1991, 15, 1072, {1, 3, 1, 15, 1, 31, 77, 207, 445, 217, 337, 1355, 7057, 6147, 24061}},
    {1992, 15, 1084, {1, 1, 7, 5, 3, 19, 39, 25, 23, 49, 85, 781, 6347, 1137, 30013}},
    {1993, 15, 1089, {1, 1, 7, 13, 25, 57, 51, 111, 201, 73, 983, 931, 1085, 8227, 21791}},
    {1994, 15, 1095, {1, 1, 7, 13, 31, 41, 15, 223, 371, 117, 103, 589, 7819, 7991, 19903}},
    {1995, 15, 1114, {1, 1, 1, 3, 29, 15, 119, 229, 163, 825, 1299, 339, 5861, 13927, 9923}},
    {1996, 15, 1123, {1, 3, 1, 3, 7, 63, 31, 69, 181, 445, 1501, 663, 4915, 7387, 22065}},
    {1997, 15, 1132, {1, 1, 5, 15, 25, 19, 69, 147, 233, 713, 1697, 1685, 2705, 6261, 1805}},
    {1998, 15, 1154, {1, 3, 3, 11, 5, 21, 1, 235, 481, 349, 749, 853, 7893, 10075, 26307}},
    {1999, 15, 1156, {1, 3, 5, 11, 7, 61, 115, 133, 227, 69, 1741, 4011, 1911, 4579, 7941}},
    {2000, 15, 1163, {1, 3, 7, 13, 15, 45, 51, 127, 467, 353, 1947, 2129, 2969, 3185, 24177}},
    {2001, 15, 1171, {1, 1, 5, 11, 25, 19, 29, 105, 483, 795, 1015, 975, 7037, 11439, 7217}},
    {2002, 15, 1202, {1, 3, 7, 9, 17, 61, 121, 143, 133, 281, 1101, 3033, 1081, 5371, 13073}},
    {2003, 15, 1228, {1, 1, 7, 9, 11, 19, 7, 61, 147, 1011, 1315, 2641, 4065, 13461, 19589}},
    {2004, 15, 1239, {1, 3, 5, 3, 7, 1, 111, 123, 51, 345, 1033, 3863, 5135, 4907, 12509}},
    {2005, 15, 1255, {1, 3, 3, 7, 3, 57, 45, 207, 487, 751, 145, 3037, 1467, 8917, 20379}},
    {2006, 15, 1256, {1, 3, 3, 11, 15, 43, 123, 195, 15, 233, 1997, 2095, 2755, 16347, 3809}},
    {2007, 15, 1262, {1, 1, 7, 3, 21, 5, 17, 253, 153, 25, 563, 139, 2611, 12733, 17505}},
    {2008, 15, 1270, {1, 3, 1, 7, 27, 43, 33, 33, 489, 441, 1845, 3507, 5089, 1173, 14689}},
    {2009, 15, 1279, {1, 1, 3, 7, 19, 43, 73, 165, 159, 873, 625, 1621, 5327, 8421, 14479}},
    {2010, 15, 1308, {1, 3, 5, 7, 31, 37, 35, 195, 373, 257, 1791, 2679, 1517, 1649, 13101}},
    {2011, 15, 1322, {1, 3, 1, 15, 11, 25, 127, 105, 65, 169, 931, 2445, 2953, 11405, 12267}},
    {2012, 15, 1329, {1, 3, 7, 9, 25, 49, 1, 25, 273, 405, 1401, 265, 1449, 8641, 31469}},
    {2014, 15, 1330, {1, 3, 3, 9, 23, 3, 5, 99, 439, 521, 317, 1397, 6933, 14937, 15165}},
    {2014, 15, 1336, {1, 1, 1, 5, 1, 25, 9, 137, 173, 1003, 625, 2783, 4179, 6203, 29619}},
    {2015, 15, 1341, {1, 3, 7, 1, 7, 31, 49, 251, 269, 107, 659, 1091, 3833, 2803, 11677}},
    {2016, 15, 1347, {1, 1, 7, 5, 1, 25, 79, 255, 335, 585, 457, 2331, 3371, 12899, 8727}},
    {2017, 15, 1349, {1, 1, 1, 9, 21, 37, 35, 115, 197, 587, 81, 2641, 3343, 10733, 17601}},
    {2018, 15, 1359, {1, 1, 5, 1, 21, 9, 39, 95, 47, 289, 355, 183, 5063, 7409, 11539}},
    {2019, 15, 1367, {1, 3, 1, 3, 23, 23, 11, 165, 65, 51, 597, 1657, 4625, 6489, 21539}},
    {2020, 15, 1368, {1, 1, 5, 1, 27, 25, 83, 201, 445, 659, 703, 2129, 5537, 8669, 10197}},
    {2021, 15, 1390, {1, 1, 7, 11, 29, 17, 27, 205, 321, 117, 1519, 3543, 1025, 9761, 3193}},
    {2022, 15, 1413, {1, 3, 1, 13, 7, 17, 109, 3, 243, 495, 1541, 2153, 3391, 10359, 31065}},
    {2023, 15, 1414, {1, 1, 7, 7, 19, 35, 79, 229, 413, 967, 1917, 1363, 5967, 8581, 6219}},
    {2024, 15, 1437, {1, 3, 5, 7, 9, 25, 23, 187, 445, 879, 773, 3335, 7989, 16287, 20037}},
    {2025, 15, 1441, {1, 3, 3, 15, 3, 1, 43, 99, 189, 567, 49, 3215, 3375, 1523, 7707}},
    {2026, 15, 1462, {1, 3, 5, 5, 19, 37, 109, 173, 301, 35, 1231, 1891, 7891, 4673, 8549}},
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    {2028, 15, 1480, {1, 3, 5, 13, 21, 23, 113, 187, 59, 103, 1339, 3811, 3527, 1267, 26137}},
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    {2030, 15, 1504, {1, 3, 7, 15, 11, 55, 35, 51, 387, 585, 1919, 753, 6919, 10933, 11737}},
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    {2034, 15, 1528, {1, 1, 5, 5, 11, 31, 63, 127, 273, 549, 181, 273, 581, 3167, 13969}},
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    {2040, 15, 1588, {1, 1, 5, 15, 5, 3, 91, 25, 477, 399, 319, 3321, 515, 5445, 24811}},
    {2041, 15, 1603, {1, 3, 7, 13, 31, 27, 17, 137, 503, 143, 1485, 703, 179, 13787, 5227}},
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    {2044, 15, 1620, {1, 3, 1, 3, 25, 15, 61, 51, 5, 41, 1563, 2719, 5695, 4625, 22765}},
    {2045, 15, 1629, {1, 3, 5, 15, 23, 33, 13, 17, 385, 153, 107, 1935, 5465, 12201, 7447}},
    {2046, 15, 1636, {1, 3, 3, 7, 31, 13, 81, 55, 499, 639, 1455, 3983, 7, 11453, 5179}},
    {2047, 15, 1648, {1, 3, 5, 5, 1, 15, 15, 129, 441, 825, 1985, 3811, 149, 7375, 8407}},
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    {2049, 15, 1669, {1, 3, 7, 9, 29, 13, 39, 15, 417, 943, 1477, 1053, 6305, 9087, 29601}},
    {2050, 15, 1682, {1, 3, 5, 9, 7, 1, 45, 253, 305, 379, 501, 1873, 7507, 11075, 23027}},
    {2051, 15, 1697, {1, 1, 3, 1, 17, 61, 25, 199, 207, 331, 819, 3617, 365, 4233, 1639}},
    {2052, 15, 1704, {1, 3, 1, 15, 25, 17, 25, 145, 189, 599, 891, 3475, 563, 3197, 7873}},
    {2053, 15, 1709, {1, 1, 5, 7, 19, 59, 5, 35, 207, 425, 767, 3217, 7583, 4351, 11627}},
    {2054, 15, 1727, {1, 1, 5, 11, 3, 43, 105, 197, 455, 315, 1601, 1125, 1823, 1515, 2179}},
    {2055, 15, 1730, {1, 3, 5, 3, 25, 7, 97, 69, 487, 407, 1599, 1087, 3083, 7445, 1369}},
    {2056, 15, 1732, {1, 1, 7, 11, 13, 47, 25, 115, 225, 11, 311, 3037, 2607, 1015, 15603}},
    {2057, 15, 1741, {1, 1, 5, 3, 19, 49, 7, 59, 469, 431, 387, 1909, 983, 1751, 30221}},
    {2058, 15, 1744, {1, 3, 5, 3, 23, 51, 65, 19, 221, 665, 155, 1323, 1497, 10815, 20521}},
    {2059, 15, 1759, {1, 3, 1, 1, 3, 51, 67, 149, 373, 165, 1923, 1043, 3819, 7405, 6115}},
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    {2061, 15, 1766, {1, 1, 3, 5, 1, 29, 43, 111, 423, 411, 1119, 2719, 4063, 8179, 6727}},
    {2062, 15, 1778, {1, 1, 7, 13, 15, 43, 57, 249, 503, 41, 1533, 1657, 7715, 1761, 24099}},
    {2063, 15, 1780, {1, 1, 1, 11, 27, 23, 51, 131, 479, 495, 1843, 2099, 1551, 957, 14961}},
    {2064, 15, 1783, {1, 3, 7, 15, 7, 47, 63, 51, 433, 429, 27, 3511, 4209, 3735, 21843}},
    {2065, 15, 1797, {1, 3, 3, 3, 19, 9, 39, 207, 191, 77, 1449, 3817, 2389, 5971, 763}},
    {2066, 15, 1807, {1, 3, 3, 3, 13, 9, 123, 253, 279, 515, 1099, 2511, 1233, 12429, 24569}},
    {2067, 15, 1821, {1, 1, 3, 1, 27, 11, 17, 167, 385, 125, 253, 2869, 3583, 16219, 26881}},
    {2068, 15, 1832, {1, 3, 3, 3, 25, 35, 89, 131, 61, 941, 33, 267, 1399, 8411, 1321}},
    {2069, 15, 1835, {1, 3, 5, 15, 3, 1, 109, 61, 499, 81, 1085, 3787, 139, 9827, 12999}},
    {2070, 15, 1849, {1, 3, 3, 1, 23, 61, 35, 145, 325, 865, 699, 33, 2391, 3707, 14153}},
    {2071, 15, 1850, {1, 1, 5, 13, 7, 61, 101, 47, 303, 477, 375, 87, 3689, 1803, 18173}},
    {2072, 15, 1863, {1, 3, 5, 5, 9, 61, 51, 171, 21, 285, 345, 2801, 1113, 7593, 16085}},
    {2073, 15, 1867, {1, 3, 1, 15, 27, 25, 121, 235, 505, 575, 1595, 747, 3295, 10725, 11769}},
    {2074, 15, 1869, {1, 1, 7, 9, 1, 25, 91, 231, 257, 539, 831, 3109, 7933, 2539, 30833}},
    {2075, 15, 1872, {1, 1, 1, 13, 25, 5, 51, 137, 145, 705, 1533, 647, 3539, 12305, 6663}},
    {2076, 15, 1887, {1, 3, 3, 7, 9, 47, 119, 109, 351, 167, 375, 3671, 1655, 3971, 7261}},
    {2077, 15, 1888, {1, 3, 1, 11, 19, 39, 69, 135, 159, 1007, 749, 879, 1923, 1993, 16949}},
    {2078, 15, 1897, {1, 3, 1, 11, 7, 37, 119, 237, 327, 57, 785, 1013, 3801, 14421, 21685}},
    {2079, 15, 1906, {1, 3, 5, 15, 11, 53, 27, 199, 137, 981, 511, 897, 7467, 6827, 28783}},
    {2080, 15, 1917, {1, 3, 7, 3, 17, 47, 9, 145, 153, 105, 1661, 1145, 2671, 15261, 6579}},
    {2081, 15, 1927, {1, 3, 5, 9, 7, 59, 101, 151, 51, 907, 1201, 2359, 6907, 4039, 26507}},
    {2082, 15, 1939, {1, 3, 7, 9, 27, 39, 89, 249, 165, 655, 847, 2321, 7287, 15655, 21707}},
    {2083, 15, 1941, {1, 3, 3, 3, 27, 37, 113, 121, 379, 763, 1955, 1329, 6435, 10091, 8779}},
    {2084, 15, 1948, {1, 1, 7, 9, 27, 43, 17, 37, 313, 663, 801, 2685, 6249, 10353, 31151}},
    {2085, 15, 1970, {1, 1, 7, 3, 25, 7, 5, 207, 71, 427, 1739, 463, 6785, 4159, 1809}},
    {2086, 15, 1979, {1, 1, 7, 13, 7, 41, 125, 27, 357, 343, 1093, 2569, 2991, 395, 18383}},
    {2087, 15, 1982, {1, 3, 1, 3, 29, 17, 87, 73, 85, 273, 1175, 2825, 4727, 10575, 315}},
    {2088, 15, 2002, {1, 3, 3, 7, 31, 35, 87, 27, 11, 423, 1817, 723, 6049, 4513, 17499}},
    {2089, 15, 2020, {1, 1, 5, 7, 23, 31, 123, 195, 453, 581, 371, 195, 1417, 10659, 28837}},
    {2090, 15, 2024, {1, 1, 5, 9, 1, 29, 77, 21, 291, 999, 203, 795, 4563, 15141, 5313}},
    {2091, 15, 2032, {1, 3, 1, 5, 15, 25, 119, 211, 289, 255, 1183, 3261, 7841, 1729, 16521}},
    {2092, 15, 2053, {1, 1, 5, 3, 27, 9, 67, 157, 7, 141, 187, 1031, 7535, 8651, 31595}},
    {2093, 15, 2060, {1, 3, 7, 11, 11, 63, 111, 73, 453, 259, 1963, 2845, 2971, 10815, 12389}},
    {2094, 15, 2063, {1, 3, 3, 7, 9, 51, 91, 231, 455, 379, 1445, 1985, 2209, 16327, 16303}},
    {2095, 15, 2066, {1, 3, 3, 7, 21, 1, 29, 231, 405, 263, 847, 3885, 3487, 11779, 30607}},
    {2096, 15, 2075, {1, 1, 5, 11, 29, 33, 81, 139, 119, 43, 1257, 2759, 4491, 14777, 25007}},
    {2097, 15, 2078, {1, 1, 1, 15, 1, 45, 87, 15, 363, 571, 2025, 3707, 4701, 6465, 24497}},
    {2098, 15, 2081, {1, 1, 7, 7, 29, 15, 115, 29, 35, 227, 1669, 2409, 4889, 6825, 31695}},
    {2099, 15, 2091, {1, 3, 5, 1, 11, 17, 1, 17, 47, 737, 1417, 855, 4697, 2555, 5721}},
    {2100, 15, 2096, {1, 3, 3, 1, 21, 59, 29, 5, 387, 173, 147, 2845, 2289, 299, 6867}},
    {2101, 15, 2102, {1, 3, 5, 7, 3, 41, 87, 97, 135, 995, 1227, 3527, 5611, 7537, 27221}},
    {2102, 15, 2106, {1, 3, 5, 3, 29, 63, 9, 83, 13, 289, 1009, 3281, 2809, 11533, 12153}},
    {2103, 15, 2116, {1, 3, 5, 15, 9, 63, 99, 219, 289, 731, 1345, 3883, 179, 6209, 20605}},
    {2104, 15, 2120, {1, 3, 5, 1, 31, 29, 59, 197, 511, 719, 361, 2235, 1429, 14139, 26365}},
    {2105, 15, 2125, {1, 3, 5, 11, 13, 3, 17, 1, 377, 955, 1331, 2059, 2177, 15579, 4899}},
    {2106, 15, 2134, {1, 3, 7, 11, 25, 19, 93, 9, 173, 167, 1721, 517, 8053, 5459, 16839}},
    {2107, 15, 2178, {1, 3, 1, 3, 21, 21, 7, 237, 135, 173, 235, 101, 7101, 9351, 30381}},
    {2108, 15, 2180, {1, 1, 7, 9, 27, 39, 87, 17, 27, 9, 1829, 3031, 4807, 1241, 7225}},
    {2109, 15, 2187, {1, 1, 1, 7, 15, 27, 125, 229, 279, 795, 901, 777, 2739, 4913, 30471}},
    {2110, 15, 2189, {1, 1, 7, 3, 7, 39, 31, 239, 195, 641, 711, 3109, 587, 9745, 15467}},
    {2111, 15, 2190, {1, 3, 7, 3, 19, 63, 101, 179, 393, 501, 1297, 1761, 4251, 7963, 32109}},
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    {2113, 15, 2214, {1, 1, 7, 5, 25, 63, 17, 213, 323, 563, 1951, 1079, 5741, 6085, 23939}},
    {2114, 15, 2237, {1, 1, 3, 1, 27, 29, 15, 67, 511, 437, 1821, 2073, 1511, 291, 32149}},
    {2115, 15, 2252, {1, 1, 3, 5, 27, 45, 61, 221, 25, 741, 429, 1703, 109, 2733, 3081}},
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    {2123, 15, 2312, {1, 3, 5, 5, 5, 17, 117, 143, 65, 475, 1483, 363, 1827, 12091, 489}},
    {2124, 15, 2317, {1, 3, 5, 13, 21, 51, 35, 17, 391, 133, 291, 2625, 6355, 15173, 30837}},
    {2125, 15, 2323, {1, 1, 1, 13, 23, 7, 95, 7, 503, 965, 427, 349, 6847, 3371, 17469}},
    {2126, 15, 2329, {1, 1, 3, 11, 19, 11, 51, 79, 307, 495, 1411, 2025, 921, 8977, 11803}},
    {2127, 15, 2335, {1, 1, 5, 7, 31, 19, 71, 5, 189, 335, 1677, 3355, 5933, 1949, 15723}},
    {2128, 15, 2342, {1, 1, 7, 1, 25, 3, 49, 43, 331, 225, 983, 3249, 7263, 7519, 19271}},
    {2129, 15, 2345, {1, 1, 7, 1, 9, 9, 117, 111, 117, 925, 1339, 1933, 2809, 6951, 30905}},
    {2130, 15, 2365, {1, 3, 3, 3, 11, 31, 87, 233, 409, 9, 899, 4009, 3099, 9757, 1927}},
    {2131, 15, 2371, {1, 1, 3, 9, 23, 17, 79, 123, 221, 579, 299, 3319, 1785, 2703, 3761}},
    {2132, 15, 2378, {1, 3, 3, 9, 19, 33, 127, 85, 269, 977, 701, 523, 3611, 10055, 8135}},
    {2133, 15, 2385, {1, 3, 7, 1, 15, 5, 47, 77, 85, 475, 769, 3473, 3837, 11149, 23787}},
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    {5883, 17, 1377, {1, 1, 7, 15, 21, 9, 47, 111, 127, 229, 1583, 1311, 3035, 3877, 3525, 62965, 47477}},
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    {5950, 17, 1945, {1, 1, 1, 15, 15, 7, 61, 73, 413, 693, 1693, 1633, 3811, 9469, 17735, 35407, 121389}},
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    {5953, 17, 1975, {1, 3, 3, 11, 5, 13, 47, 97, 265, 719, 1765, 1009, 7841, 893, 27067, 28465, 5573}},
    {5954, 17, 1976, {1, 1, 7, 1, 7, 29, 121, 209, 283, 495, 1367, 1089, 2519, 6965, 16875, 56481, 110483}},
    {5955, 17, 1987, {1, 1, 3, 13, 11, 61, 7, 179, 295, 715, 579, 2805, 4007, 14819, 12575, 25637, 4871}},
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    {5960, 17, 2030, {1, 3, 1, 5, 3, 53, 127, 139, 29, 399, 2023, 3705, 3381, 545, 26255, 4473, 43667}},
    {5961, 17, 2038, {1, 1, 3, 13, 25, 19, 19, 123, 321, 751, 1499, 4025, 4253, 6219, 25039, 245, 72777}},
    {5962, 17, 2041, {1, 3, 5, 5, 31, 39, 5, 207, 413, 523, 1965, 1875, 6681, 5129, 25525, 44591, 42689}},
    {5963, 17, 2048, {1, 1, 1, 5, 25, 45, 47, 119, 123, 89, 779, 1371, 5151, 16343, 29037, 14395, 114981}},
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    {5973, 17, 2087, {1, 1, 3, 3, 3, 1, 67, 55, 407, 167, 95, 2067, 589, 4141, 6139, 61253, 55169}},
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    {5975, 17, 2111, {1, 3, 7, 11, 31, 7, 77, 121, 469, 29, 651, 2675, 4559, 6279, 27223, 52091, 129843}},
    {5976, 17, 2113, {1, 1, 3, 11, 17, 47, 5, 221, 497, 771, 1399, 4055, 4841, 3929, 7285, 52605, 91391}},
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    {5982, 17, 2177, {1, 3, 1, 13, 21, 5, 61, 241, 235, 737, 667, 3119, 825, 6097, 1729, 5561, 88423}},
    {5983, 17, 2178, {1, 3, 5, 9, 25, 1, 57, 59, 435, 29, 1473, 2789, 103, 7459, 5285, 26615, 36497}},
    {5984, 17, 2184, {1, 1, 3, 9, 11, 47, 123, 63, 309, 505, 1735, 637, 1915, 5729, 26343, 42547, 86783}},
    {5985, 17, 2198, {1, 1, 1, 3, 13, 41, 15, 93, 507, 793, 1635, 3021, 4803, 15761, 13589, 60039, 11647}},
    {5986, 17, 2201, {1, 3, 5, 15, 27, 49, 55, 219, 185, 817, 1959, 3023, 3105, 12443, 30191, 30671, 1601}},
    {5987, 17, 2213, {1, 1, 3, 1, 17, 15, 13, 133, 403, 155, 29, 3587, 229, 8811, 4967, 12633, 31213}},
    {5988, 17, 2217, {1, 3, 1, 3, 15, 11, 41, 177, 191, 523, 541, 3691, 5353, 131, 7261, 17133, 75713}},
    {5989, 17, 2228, {1, 1, 3, 7, 1, 23, 33, 163, 207, 475, 1145, 3811, 7407, 2793, 19647, 49395, 81739}},
    {5990, 17, 2240, {1, 3, 7, 11, 11, 47, 105, 39, 509, 579, 959, 1427, 5533, 10283, 22477, 9159, 35261}},
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    {5992, 17, 2250, {1, 3, 3, 15, 27, 9, 27, 209, 389, 737, 1479, 4065, 5237, 4207, 12695, 28619, 98073}},
    {5993, 17, 2263, {1, 3, 7, 13, 23, 21, 3, 109, 453, 17, 1097, 2113, 5163, 5535, 2471, 52965, 61345}},
    {5994, 17, 2267, {1, 1, 7, 7, 23, 13, 43, 245, 421, 245, 801, 3853, 2965, 16139, 23697, 15625, 102399}},
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    {6025, 17, 2518, {1, 3, 7, 13, 29, 19, 97, 85, 251, 799, 1813, 1081, 309, 15483, 12815, 55065, 5761}},
    {6026, 17, 2527, {1, 1, 7, 7, 5, 31, 71, 65, 69, 243, 341, 2219, 267, 1657, 14251, 28923, 73929}},
    {6027, 17, 2540, {1, 1, 1, 5, 23, 21, 115, 137, 413, 545, 1015, 867, 7461, 5001, 1809, 6579, 26067}},
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    {10059, 17, 36839, {1, 1, 3, 9, 3, 25, 3, 55, 269, 87, 251, 3005, 3539, 2397, 16187, 61041, 120715}},
    {10060, 17, 36843, {1, 3, 1, 1, 23, 23, 13, 231, 477, 19, 1313, 1065, 6755, 10711, 21115, 63893, 52939}},
    {10061, 17, 36860, {1, 1, 7, 1, 25, 27, 127, 37, 489, 677, 1857, 2853, 6691, 14447, 25243, 61797, 109587}},
    {10062, 17, 36866, {1, 3, 5, 9, 13, 7, 85, 231, 281, 1015, 829, 1659, 2259, 10725, 22391, 55987, 58811}},
    {10063, 17, 36871, {1, 1, 7, 9, 13, 33, 51, 101, 107, 195, 255, 3893, 3939, 14219, 25995, 63501, 96483}},
    {10064, 17, 36875, {1, 3, 5, 15, 13, 17, 115, 195, 341, 97, 995, 641, 2373, 10921, 30971, 57463, 16657}},
    {10065, 17, 36877, {1, 3, 7, 3, 17, 57, 121, 147, 423, 925, 961, 3837, 7551, 12065, 13783, 35679, 51365}},
    {10066, 17, 36880, {1, 3, 5, 11, 19, 27, 35, 179, 441, 397, 603, 2935, 7741, 2041, 30259, 9589, 113541}},
    {10067, 17, 36892, {1, 3, 5, 3, 27, 13, 79, 91, 83, 579, 203, 683, 3163, 8391, 4849, 64795, 26011}},
    {10068, 17, 36911, {1, 3, 7, 7, 31, 33, 31, 121, 17, 871, 1563, 1673, 2587, 11209, 1633, 27517, 76227}},
    {10069, 17, 36914, {1, 1, 7, 1, 15, 31, 79, 37, 217, 829, 1439, 1885, 2517, 3375, 3521, 44845, 119393}},
    {10070, 17, 36916, {1, 3, 5, 13, 25, 25, 77, 89, 331, 471, 1323, 353, 3409, 6953, 17551, 36643, 100673}},
    {10071, 17, 36923, {1, 1, 3, 5, 25, 11, 65, 57, 301, 695, 221, 2313, 7423, 5879, 32453, 14197, 89303}},
    {10072, 17, 36940, {1, 3, 1, 7, 11, 61, 59, 219, 273, 931, 1311, 1203, 6965, 3479, 26721, 40719, 62397}},
    {10073, 17, 36943, {1, 1, 5, 13, 23, 9, 101, 173, 261, 433, 1375, 2721, 1587, 12531, 20877, 17275, 68839}},
    {10074, 17, 36948, {1, 3, 7, 5, 15, 45, 89, 157, 129, 623, 1307, 3493, 3383, 11561, 28771, 50823, 50099}},
    {10075, 17, 36957, {1, 3, 7, 5, 3, 41, 103, 55, 193, 361, 1421, 2239, 6049, 2245, 26757, 64233, 3933}},
    {10076, 17, 36958, {1, 1, 5, 9, 11, 15, 115, 195, 17, 743, 2005, 3345, 5753, 14603, 29229, 11199, 58937}},
    {10077, 17, 36967, {1, 3, 7, 3, 31, 61, 43, 177, 485, 711, 79, 3387, 8065, 5135, 5421, 35607, 32783}},
    {10078, 17, 36974, {1, 3, 1, 11, 29, 61, 73, 93, 157, 405, 1843, 1125, 7071, 4009, 16643, 21253, 117935}},
    {10079, 17, 36981, {1, 1, 3, 1, 15, 21, 83, 105, 123, 297, 309, 2275, 763, 9069, 28451, 32729, 124591}},
    {10080, 17, 37001, {1, 1, 7, 11, 13, 51, 35, 7, 485, 905, 465, 163, 1007, 5923, 13559, 5575, 102755}},
    {10081, 17, 37012, {1, 3, 7, 7, 3, 57, 69, 217, 209, 341, 1591, 3151, 3575, 1787, 30335, 44377, 82517}},
    {10082, 17, 37015, {1, 1, 3, 15, 7, 37, 121, 77, 97, 99, 1499, 349, 4205, 16229, 31279, 32539, 18057}},
    {10083, 17, 37019, {1, 1, 7, 11, 23, 59, 83, 77, 11, 413, 1379, 3875, 851, 10949, 24169, 24495, 27945}},
    {10084, 17, 37035, {1, 1, 3, 9, 23, 1, 9, 239, 343, 37, 229, 751, 7525, 7333, 11653, 10529, 122991}},
    {10085, 17, 37040, {1, 3, 3, 9, 23, 3, 69, 129, 179, 519, 1949, 2933, 439, 9925, 12635, 18005, 3009}},
    {10086, 17, 37063, {1, 3, 1, 13, 17, 1, 109, 43, 313, 865, 1713, 3329, 167, 6203, 14915, 40173, 83181}},
    {10087, 17, 37064, {1, 1, 1, 9, 3, 29, 43, 101, 445, 295, 269, 3637, 7333, 10677, 14777, 44203, 36491}},
    {10088, 17, 37069, {1, 1, 3, 1, 29, 47, 49, 157, 99, 1015, 525, 2265, 4217, 1493, 21367, 28015, 115923}},
    {10089, 17, 37077, {1, 1, 3, 11, 31, 15, 19, 85, 491, 23, 283, 139, 3715, 2197, 7563, 50881, 29255}},
    {10090, 17, 37093, {1, 3, 3, 9, 27, 29, 123, 193, 417, 509, 531, 1969, 2627, 15557, 30429, 61599, 91847}},
    {10091, 17, 37097, {1, 3, 5, 11, 1, 21, 109, 177, 427, 303, 303, 1215, 3, 2745, 17931, 49221, 92711}},
    {10092, 17, 37106, {1, 1, 3, 1, 27, 5, 103, 183, 453, 811, 1051, 769, 8121, 10643, 1633, 30395, 4625}},
    {10093, 17, 37115, {1, 1, 3, 15, 11, 3, 127, 57, 501, 849, 1355, 19, 1083, 2143, 10763, 32603, 79497}},
    {10094, 17, 37118, {1, 1, 7, 9, 21, 51, 61, 87, 29, 281, 1159, 469, 6935, 1587, 21883, 16245, 126065}},
    {10095, 17, 37123, {1, 1, 1, 13, 27, 15, 31, 47, 325, 125, 1275, 2417, 1633, 12669, 4149, 23085, 99825}},
    {10096, 17, 37129, {1, 3, 5, 13, 31, 25, 93, 235, 453, 61, 1051, 1121, 1241, 11843, 25947, 7881, 119051}},
    {10097, 17, 37130, {1, 3, 7, 13, 13, 17, 19, 175, 175, 407, 1119, 781, 7891, 10293, 30503, 45905, 111399}},
    {10098, 17, 37135, {1, 1, 1, 11, 19, 39, 59, 17, 475, 669, 323, 3627, 8087, 1057, 25691, 26351, 128137}},
    {10099, 17, 37137, {1, 3, 5, 9, 5, 61, 79, 241, 85, 543, 215, 887, 4977, 3797, 8469, 35043, 79153}},
    {10100, 17, 37138, {1, 3, 7, 13, 11, 45, 45, 75, 177, 537, 1197, 1721, 8013, 13659, 19085, 17365, 83679}},
    {10101, 17, 37140, {1, 3, 5, 15, 17, 15, 107, 33, 57, 1009, 577, 3755, 8055, 15965, 5447, 979, 7737}},
    {10102, 17, 37144, {1, 3, 7, 7, 15, 19, 61, 225, 75, 195, 457, 1881, 6865, 9037, 12353, 24127, 50881}},
    {10103, 17, 37149, {1, 1, 1, 9, 11, 39, 3, 173, 67, 403, 55, 2227, 1407, 1003, 1725, 33271, 128721}},
    {10104, 17, 37156, {1, 3, 5, 3, 21, 17, 31, 99, 275, 327, 879, 2939, 1529, 9589, 803, 30549, 118977}},
    {10105, 17, 37159, {1, 3, 3, 1, 17, 43, 1, 195, 205, 979, 679, 699, 6903, 5637, 9411, 22843, 8879}},
    {10106, 17, 37163, {1, 3, 1, 5, 27, 29, 25, 145, 433, 723, 1185, 1283, 197, 3389, 3761, 24925, 60855}},
    {10107, 17, 37165, {1, 1, 3, 1, 15, 35, 127, 151, 327, 903, 641, 1507, 5, 1269, 29599, 10273, 38277}},
    {10108, 17, 37183, {1, 1, 5, 5, 3, 21, 111, 167, 41, 467, 803, 773, 2149, 12889, 10659, 50465, 94233}},
    {10109, 17, 37185, {1, 1, 7, 1, 17, 33, 99, 209, 351, 65, 1857, 2367, 1775, 7727, 15059, 37541, 125893}},
    {10110, 17, 37195, {1, 3, 5, 3, 11, 17, 47, 91, 115, 229, 1047, 3613, 1339, 13261, 1613, 21971, 47863}},
    {10111, 17, 37198, {1, 1, 1, 1, 11, 13, 47, 25, 229, 653, 873, 3335, 6773, 3889, 11975, 51977, 118725}},
    {10112, 17, 37203, {1, 1, 7, 5, 13, 57, 103, 101, 465, 291, 467, 2379, 7633, 14915, 2743, 32483, 71265}},
    {10113, 17, 37212, {1, 3, 3, 7, 19, 31, 125, 225, 73, 907, 1351, 3213, 6281, 1257, 20769, 45375, 8631}},
    {10114, 17, 37233, {1, 1, 1, 3, 19, 51, 117, 83, 495, 269, 939, 453, 7927, 6321, 12261, 20355, 40737}},
    {10115, 17, 37236, {1, 1, 7, 15, 5, 11, 107, 209, 503, 333, 1317, 2419, 2291, 1835, 17773, 54467, 54355}},
    {10116, 17, 37240, {1, 1, 7, 13, 7, 55, 49, 193, 271, 821, 103, 2551, 4089, 7225, 17055, 37139, 114215}},
    {10117, 17, 37256, {1, 1, 3, 15, 13, 21, 109, 75, 159, 711, 645, 3363, 2595, 6665, 411, 21815, 121545}},
    {10118, 17, 37264, {1, 3, 1, 3, 11, 31, 31, 175, 277, 537, 2035, 2649, 4629, 4765, 17291, 58759, 10223}},
    {10119, 17, 37267, {1, 1, 7, 3, 9, 21, 57, 181, 285, 667, 109, 3247, 6881, 3713, 3667, 33743, 105161}},
    {10120, 17, 37273, {1, 3, 5, 5, 1, 63, 51, 69, 293, 519, 1297, 3073, 7659, 829, 25307, 2187, 32613}},
    {10121, 17, 37295, {1, 1, 5, 9, 11, 57, 29, 193, 427, 709, 1429, 1185, 4341, 5917, 2441, 53145, 32039}},
    {10122, 17, 37315, {1, 1, 1, 7, 29, 55, 11, 71, 283, 223, 1999, 2597, 5887, 5097, 29055, 21741, 65855}},
    {10123, 17, 37330, {1, 3, 3, 7, 13, 31, 101, 211, 323, 85, 961, 2833, 4357, 1745, 14945, 7077, 104591}},
    {10124, 17, 37336, {1, 1, 3, 11, 17, 39, 125, 27, 327, 281, 87, 2341, 433, 15277, 20541, 44881, 107773}},
    {10125, 17, 37339, {1, 3, 1, 15, 31, 7, 91, 63, 349, 103, 1101, 1049, 6527, 15471, 9253, 58841, 95553}},
    {10126, 17, 37342, {1, 3, 1, 11, 9, 33, 15, 215, 141, 317, 1405, 1811, 7617, 3311, 24845, 7629, 445}},
    {10127, 17, 37357, {1, 3, 3, 3, 13, 27, 27, 123, 7, 101, 1509, 2789, 3833, 16205, 24905, 29453, 106435}},
    {10128, 17, 37365, {1, 3, 1, 13, 5, 51, 47, 87, 483, 791, 921, 4079, 6607, 14077, 1297, 41961, 86579}},
    {10129, 17, 37372, {1, 3, 7, 3, 9, 23, 83, 227, 321, 397, 1483, 1857, 7191, 9211, 4511, 7547, 82415}},
    {10130, 17, 37381, {1, 1, 7, 13, 15, 43, 47, 135, 211, 497, 1827, 2493, 2475, 2011, 25013, 44627, 13675}},
    {10131, 17, 37399, {1, 3, 3, 11, 23, 47, 73, 199, 467, 111, 27, 209, 6941, 8929, 6413, 3329, 97825}},
    {10132, 17, 37416, {1, 1, 1, 13, 31, 49, 67, 199, 229, 935, 791, 141, 2829, 11861, 9791, 15445, 17437}},
    {10133, 17, 37429, {1, 1, 5, 7, 17, 25, 47, 23, 313, 59, 371, 3865, 5767, 6461, 2973, 10165, 48247}},
    {10134, 17, 37436, {1, 3, 7, 3, 25, 47, 37, 51, 371, 101, 249, 91, 3985, 10239, 10423, 33433, 109067}},
    {10135, 17, 37442, {1, 3, 1, 3, 27, 33, 67, 75, 167, 961, 493, 1875, 4005, 13019, 27085, 17967, 107771}},
    {10136, 17, 37451, {1, 1, 1, 3, 17, 23, 37, 179, 459, 907, 55, 2049, 5273, 4059, 30429, 10273, 70159}},
    {10137, 17, 37453, {1, 1, 5, 9, 13, 33, 71, 143, 325, 767, 1871, 3989, 7991, 3555, 28937, 48259, 60243}},
    {10138, 17, 37475, {1, 1, 1, 9, 25, 27, 111, 43, 265, 11, 1443, 3161, 3473, 1451, 3789, 42431, 117069}},
    {10139, 17, 37482, {1, 1, 1, 1, 29, 1, 121, 25, 501, 781, 1429, 1495, 6125, 11293, 30063, 1713, 7071}},
    {10140, 17, 37489, {1, 1, 3, 15, 23, 27, 15, 145, 255, 207, 1977, 567, 469, 11589, 1535, 61637, 89569}},
    {10141, 17, 37490, {1, 3, 5, 5, 13, 45, 113, 215, 65, 531, 335, 1275, 53, 447, 24887, 29829, 33391}},
    {10142, 17, 37523, {1, 1, 1, 3, 5, 55, 89, 97, 197, 467, 95, 2603, 7789, 13289, 29911, 21935, 122947}},
    {10143, 17, 37525, {1, 1, 3, 11, 21, 3, 61, 9, 363, 417, 1027, 2457, 3169, 11207, 27551, 41991, 71381}},
    {10144, 17, 37530, {1, 3, 5, 11, 19, 57, 107, 29, 249, 93, 1235, 1239, 6491, 14695, 2407, 41513, 25779}},
    {10145, 17, 37535, {1, 1, 3, 13, 5, 43, 3, 247, 309, 553, 1349, 2693, 7609, 10099, 13021, 32371, 27705}},
    {10146, 17, 37539, {1, 1, 3, 11, 7, 3, 37, 209, 153, 945, 459, 3281, 6749, 12267, 17103, 58285, 115593}},
    {10147, 17, 37548, {1, 3, 1, 3, 19, 19, 113, 23, 363, 147, 203, 1673, 4005, 4983, 31463, 12695, 95089}},
    {10148, 17, 37559, {1, 3, 5, 9, 3, 31, 77, 129, 217, 395, 1701, 15, 8181, 2327, 12441, 52889, 114339}},
    {10149, 17, 37560, {1, 1, 1, 15, 5, 7, 81, 191, 45, 45, 903, 2561, 1303, 13435, 321, 41897, 79013}},
    {10150, 17, 37566, {1, 3, 3, 13, 19, 33, 11, 67, 9, 649, 217, 2181, 2237, 2851, 7423, 37003, 119205}},
    {10151, 17, 37597, {1, 3, 7, 11, 29, 5, 87, 117, 487, 693, 155, 3653, 1497, 10249, 31567, 5987, 59435}},
    {10152, 17, 37601, {1, 3, 7, 5, 11, 5, 77, 251, 399, 257, 1429, 3487, 8097, 1919, 11635, 3833, 43577}},
    {10153, 17, 37602, {1, 1, 7, 11, 21, 63, 83, 17, 83, 807, 1849, 639, 7453, 15427, 2617, 21403, 4131}},
    {10154, 17, 37604, {1, 1, 7, 15, 19, 1, 43, 245, 89, 271, 635, 227, 5977, 6985, 3239, 44639, 50959}},
    {10155, 17, 37616, {1, 3, 7, 1, 19, 25, 35, 41, 455, 919, 101, 1953, 6119, 15299, 16315, 58857, 107557}},
    {10156, 17, 37622, {1, 1, 5, 5, 3, 27, 123, 81, 355, 327, 1645, 1439, 3497, 3133, 17, 7225, 83255}},
    {10157, 17, 37658, {1, 1, 1, 15, 29, 31, 61, 15, 157, 161, 1751, 2687, 3539, 5695, 149, 8841, 23405}},
    {10158, 17, 37660, {1, 1, 1, 15, 1, 27, 79, 231, 157, 275, 1687, 3083, 4547, 9929, 6181, 32653, 30727}},
    {10159, 17, 37667, {1, 1, 1, 1, 29, 51, 95, 133, 311, 675, 1829, 2089, 7681, 13119, 32157, 10651, 9023}},
    {10160, 17, 37684, {1, 3, 5, 11, 7, 11, 41, 137, 147, 623, 81, 253, 3159, 4501, 22465, 41047, 14253}},
    {10161, 17, 37693, {1, 1, 5, 15, 9, 29, 35, 63, 265, 691, 1371, 4061, 6327, 10671, 9303, 58831, 122423}},
    {10162, 17, 37694, {1, 3, 3, 13, 17, 43, 9, 173, 435, 805, 1679, 3261, 6681, 13295, 23511, 4575, 100573}},
    {10163, 17, 37696, {1, 1, 3, 15, 7, 11, 93, 227, 285, 795, 1089, 927, 2187, 927, 4283, 29241, 75241}},
    {10164, 17, 37706, {1, 1, 1, 7, 13, 7, 71, 167, 239, 411, 235, 1543, 5259, 9749, 4257, 30517, 18167}},
    {10165, 17, 37711, {1, 1, 7, 7, 29, 37, 67, 245, 151, 627, 1245, 2967, 7821, 1113, 3243, 59403, 80303}},
    {10166, 17, 37730, {1, 1, 5, 13, 31, 15, 9, 49, 81, 257, 31, 227, 201, 2127, 30581, 38487, 96959}},
    {10167, 17, 37735, {1, 1, 5, 5, 21, 39, 61, 155, 47, 235, 355, 3397, 2973, 1029, 23497, 21007, 35183}},
    {10168, 17, 37742, {1, 1, 3, 5, 7, 27, 87, 45, 89, 211, 519, 2621, 6299, 2049, 21225, 4975, 8799}},
    {10169, 17, 37744, {1, 3, 5, 11, 7, 51, 19, 33, 153, 925, 1067, 3789, 7463, 8403, 1495, 37549, 20661}},
    {10170, 17, 37759, {1, 1, 5, 1, 21, 53, 97, 147, 435, 329, 1635, 3069, 3353, 3969, 15555, 7171, 58141}},
    {10171, 17, 37777, {1, 1, 1, 5, 31, 29, 103, 87, 89, 673, 1505, 2921, 3019, 3081, 7723, 11105, 7477}},
    {10172, 17, 37783, {1, 1, 7, 5, 17, 15, 111, 15, 59, 851, 1351, 2365, 2427, 5035, 22341, 38511, 61813}},
    {10173, 17, 37784, {1, 3, 5, 9, 21, 15, 35, 11, 149, 991, 981, 3855, 2783, 10405, 21113, 64173, 75199}},
    {10174, 17, 37793, {1, 3, 5, 7, 19, 25, 99, 11, 101, 71, 1913, 1017, 4241, 15635, 15571, 33541, 79103}},
    {10175, 17, 37800, {1, 3, 7, 9, 13, 19, 67, 75, 57, 257, 1623, 3641, 1745, 12747, 7171, 20861, 106387}},
    {10176, 17, 37818, {1, 3, 1, 3, 9, 43, 29, 125, 453, 525, 1789, 2281, 1037, 14799, 27183, 7235, 97467}},
    {10177, 17, 37823, {1, 3, 3, 15, 25, 19, 115, 73, 163, 557, 1365, 1205, 7845, 2977, 6293, 4039, 100505}},
    {10178, 17, 37825, {1, 3, 7, 15, 11, 43, 109, 181, 153, 809, 25, 773, 3265, 6919, 23835, 63627, 79707}},
    {10179, 17, 37828, {1, 3, 5, 13, 13, 9, 37, 209, 117, 49, 973, 2547, 2035, 7595, 15029, 9035, 83281}},
    {10180, 17, 37832, {1, 3, 7, 1, 1, 53, 77, 213, 137, 321, 2031, 3373, 4457, 15395, 3301, 11631, 30925}},
    {10181, 17, 37849, {1, 3, 5, 9, 21, 1, 39, 227, 1, 395, 1191, 1029, 6467, 11219, 32063, 1347, 98889}},
    {10182, 17, 37856, {1, 3, 5, 15, 21, 21, 49, 169, 289, 785, 151, 2309, 7475, 4065, 17553, 35213, 63947}},
    {10183, 17, 37861, {1, 1, 7, 13, 27, 1, 93, 245, 389, 211, 285, 1273, 6445, 4293, 53, 22689, 24989}},
    {10184, 17, 37862, {1, 3, 5, 13, 27, 27, 37, 217, 225, 271, 9, 2547, 3381, 1599, 459, 19337, 125349}},
    {10185, 17, 37886, {1, 3, 3, 5, 29, 45, 93, 239, 403, 985, 901, 3501, 1889, 15647, 25031, 6073, 14101}},
    {10186, 17, 37893, {1, 3, 1, 9, 21, 5, 77, 171, 197, 677, 1571, 3925, 4917, 14415, 20147, 39871, 125939}},
    {10187, 17, 37915, {1, 1, 5, 3, 3, 17, 19, 47, 499, 397, 667, 3373, 1771, 4453, 9519, 48939, 121915}},
    {10188, 17, 37922, {1, 3, 3, 5, 29, 25, 121, 133, 367, 281, 131, 1115, 6359, 9621, 31137, 58021, 27117}},
    {10189, 17, 37936, {1, 1, 3, 5, 23, 43, 45, 41, 261, 681, 1177, 2007, 5441, 1507, 11579, 54001, 69625}},
    {10190, 17, 37939, {1, 3, 1, 3, 27, 61, 85, 167, 275, 285, 1, 919, 6439, 3331, 9483, 46613, 89019}},
    {10191, 17, 37945, {1, 1, 7, 9, 25, 33, 37, 33, 211, 221, 273, 2257, 6565, 15801, 4911, 1781, 60147}},
    {10192, 17, 37956, {1, 3, 5, 7, 7, 17, 81, 215, 511, 565, 327, 3327, 1439, 1573, 8959, 30037, 95635}},
    {10193, 17, 37960, {1, 3, 5, 13, 23, 31, 75, 93, 421, 439, 2033, 2677, 593, 2729, 17641, 61789, 41253}},
    {10194, 17, 37971, {1, 1, 3, 11, 21, 17, 45, 63, 77, 497, 439, 4077, 4047, 273, 3233, 54695, 22014}},
    {10195, 17, 37980, {1, 3, 1, 7, 5, 17, 125, 29, 365, 887, 1915, 3455, 391, 9435, 14723, 34807, 52475}},
    {10196, 17, 38002, {1, 1, 7, 11, 29, 49, 71, 165, 491, 721, 627, 3777, 7295, 2549, 7521, 35637, 14447}},
    {10197, 17, 38007, {1, 3, 7, 13, 3, 3, 121, 193, 273, 241, 889, 13, 3445, 3313, 20381, 39921, 16609}},
    {10198, 17, 38018, {1, 3, 7, 13, 5, 49, 61, 123, 443, 769, 1669, 2741, 6881, 5965, 9365, 43051, 2979}},
    {10199, 17, 38020, {1, 1, 1, 7, 7, 25, 41, 179, 419, 225, 1827, 613, 4711, 1671, 14459, 33951, 56751}},
    {10200, 17, 38038, {1, 3, 5, 7, 9, 61, 35, 205, 243, 49, 803, 2653, 4101, 4435, 29697, 45441, 124841}}
    // Extending this table?
    // Ensure that the max_m defined in sobol_primitives.h is sufficient for all the m values
};