File: additionchains.h

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/*************************************************************************************
 *  Copyright (C) 2014 by Percy Camilo T. Aucahuasi <percy.camilo.ta@gmail.com>      *
 *                                                                                   *
 *  This program is free software; you can redistribute it and/or                    *
 *  modify it under the terms of the GNU General Public License                      *
 *  as published by the Free Software Foundation; either version 2                   *
 *  of the License, or (at your option) any later version.                           *
 *                                                                                   *
 *  This program is distributed in the hope that it will be useful,                  *
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of                   *
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                    *
 *  GNU General Public License for more details.                                     *
 *                                                                                   *
 *  You should have received a copy of the GNU General Public License                *
 *  along with this program; if not, write to the Free Software                      *
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA   *
 *************************************************************************************/

#ifndef ADDITIONCHAINS_H
#define ADDITIONCHAINS_H

//NOTE this code generates the whole thing ... 
// see seq function in 
// http://rosettacode.org/wiki/Addition-chain_exponentiation/Achain.c or
// http://www-cs-faculty.stanford.edu/~knuth/programs/achain4.w
// int main(int argc, char *argv[])
// {
//   const int MAX_N = 2048;
//   const int MAX_LEN = 15;
//   const int MAX_COL = MAX_LEN+1;
//   // seq len of max(1,2,...,MAX_N) is MAX_LEN but we need one additional slot for len (length) info (at 0) so we need MAX_COL cols
//   int buffer[MAX_N+1] = {0};
//   
//   printf("static const int additionChains[%d][%d] = {\n", MAX_N+1, MAX_COL+1);
//   for (int k = 0; k <= MAX_N; ++k) {
//     int l = k==0? 0 : k==1? 0 : seq(k, 0, buffer);
//     printf("{%d,", l);
//     
//     for (int i = 0; i < MAX_COL; ++i) {
//       if (i <= l)
//         printf("%d%s", buffer[i], i == MAX_COL-1 ? "},\n" : ",");
//       else {
//         if (k != MAX_N)
//           printf("%d%s", 0, i == MAX_COL-1 ? "},\n" : ",");
//         else
//           printf("%d%s", 0, i == MAX_COL-1 ? "}};\n" : ",");
//       }
//     }
//   }
//   
//   return 0;
// }

//NOTE we have cached 2049 sequences of addition chains (2048 plus a slot for zero)
// e.g. additionChains[124][0] is the length of a valid sequence (without 
// trailing zeros) for the number 124

const int MAX_EXPONENT = 2048;

static const int additionChains[MAX_EXPONENT+1][17] = {
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{1,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{2,1,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0},
{2,1,2,4,0,0,0,0,0,0,0,0,0,0,0,0,0},
{3,1,2,4,5,0,0,0,0,0,0,0,0,0,0,0,0},
{3,1,2,4,6,0,0,0,0,0,0,0,0,0,0,0,0},
{4,1,2,4,6,7,0,0,0,0,0,0,0,0,0,0,0},
{3,1,2,4,8,0,0,0,0,0,0,0,0,0,0,0,0},
{4,1,2,4,8,9,0,0,0,0,0,0,0,0,0,0,0},
{4,1,2,4,8,10,0,0,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,10,11,0,0,0,0,0,0,0,0,0,0},
{4,1,2,4,8,12,0,0,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,12,13,0,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,12,14,0,0,0,0,0,0,0,0,0,0},
{5,1,2,3,6,12,15,0,0,0,0,0,0,0,0,0,0},
{4,1,2,4,8,16,0,0,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,16,17,0,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,16,18,0,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,18,19,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,16,20,0,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,20,21,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,20,22,0,0,0,0,0,0,0,0,0},
{6,1,2,3,5,10,20,23,0,0,0,0,0,0,0,0,0},
{5,1,2,4,8,16,24,0,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,24,25,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,24,26,0,0,0,0,0,0,0,0,0},
{6,1,2,3,6,12,24,27,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,24,28,0,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,24,28,29,0,0,0,0,0,0,0,0},
{6,1,2,4,6,12,24,30,0,0,0,0,0,0,0,0,0},
{7,1,2,4,6,12,24,30,31,0,0,0,0,0,0,0,0},
{5,1,2,4,8,16,32,0,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,32,33,0,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,32,34,0,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,34,35,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,32,36,0,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,36,37,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,36,38,0,0,0,0,0,0,0,0},
{7,1,2,3,6,12,24,36,39,0,0,0,0,0,0,0,0},
{6,1,2,4,8,16,32,40,0,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,40,41,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,40,42,0,0,0,0,0,0,0,0},
{7,1,2,3,5,10,20,40,43,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,40,44,0,0,0,0,0,0,0,0},
{7,1,2,4,5,10,20,40,45,0,0,0,0,0,0,0,0},
{7,1,2,4,6,10,20,40,46,0,0,0,0,0,0,0,0},
{8,1,2,4,6,10,20,40,46,47,0,0,0,0,0,0,0},
{6,1,2,4,8,16,32,48,0,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,48,49,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,48,50,0,0,0,0,0,0,0,0},
{7,1,2,3,6,12,24,48,51,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,48,52,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,48,52,53,0,0,0,0,0,0,0},
{7,1,2,4,6,12,24,48,54,0,0,0,0,0,0,0,0},
{8,1,2,4,6,12,24,48,54,55,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,48,56,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,48,56,57,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,48,56,58,0,0,0,0,0,0,0},
{8,1,2,3,6,12,14,28,56,59,0,0,0,0,0,0,0},
{7,1,2,4,8,12,24,48,60,0,0,0,0,0,0,0,0},
{8,1,2,4,8,12,24,48,60,61,0,0,0,0,0,0,0},
{8,1,2,4,8,12,24,48,60,62,0,0,0,0,0,0,0},
{8,1,2,3,6,12,24,48,60,63,0,0,0,0,0,0,0},
{6,1,2,4,8,16,32,64,0,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,64,65,0,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,64,66,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,66,67,0,0,0,0,0,0,0},
{7,1,2,4,8,16,32,64,68,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,68,69,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,68,70,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,68,70,71,0,0,0,0,0,0},
{7,1,2,4,8,16,32,64,72,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,72,73,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,72,74,0,0,0,0,0,0,0},
{8,1,2,3,6,12,24,48,72,75,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,72,76,0,0,0,0,0,0,0},
{8,1,2,4,5,9,18,36,72,77,0,0,0,0,0,0,0},
{8,1,2,4,6,12,24,48,72,78,0,0,0,0,0,0,0},
{9,1,2,4,6,12,24,48,72,78,79,0,0,0,0,0,0},
{7,1,2,4,8,16,32,64,80,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,80,81,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,80,82,0,0,0,0,0,0,0},
{8,1,2,3,5,10,20,40,80,83,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,80,84,0,0,0,0,0,0,0},
{8,1,2,4,5,10,20,40,80,85,0,0,0,0,0,0,0},
{8,1,2,4,6,10,20,40,80,86,0,0,0,0,0,0,0},
{9,1,2,4,6,10,20,40,80,86,87,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,80,88,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,80,88,89,0,0,0,0,0,0},
{8,1,2,4,8,10,20,40,80,90,0,0,0,0,0,0,0},
{9,1,2,4,8,10,20,40,80,90,91,0,0,0,0,0,0},
{8,1,2,4,8,12,20,40,80,92,0,0,0,0,0,0,0},
{9,1,2,4,8,12,20,40,80,92,93,0,0,0,0,0,0},
{9,1,2,4,8,12,20,40,80,92,94,0,0,0,0,0,0},
{9,1,2,3,5,10,20,23,46,92,95,0,0,0,0,0,0},
{7,1,2,4,8,16,32,64,96,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,96,97,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,96,98,0,0,0,0,0,0,0},
{8,1,2,3,6,12,24,48,96,99,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,96,100,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,96,100,101,0,0,0,0,0,0},
{8,1,2,4,6,12,24,48,96,102,0,0,0,0,0,0,0},
{9,1,2,4,6,12,24,48,96,102,103,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,96,104,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,96,104,105,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,96,104,106,0,0,0,0,0,0},
{9,1,2,3,6,12,24,26,52,104,107,0,0,0,0,0,0},
{8,1,2,4,8,12,24,48,96,108,0,0,0,0,0,0,0},
{9,1,2,4,8,12,24,48,96,108,109,0,0,0,0,0,0},
{9,1,2,4,8,12,24,48,96,108,110,0,0,0,0,0,0},
{9,1,2,3,6,12,24,48,96,108,111,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,96,112,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,96,112,113,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,96,112,114,0,0,0,0,0,0},
{9,1,2,3,6,12,14,28,56,112,115,0,0,0,0,0,0},
{9,1,2,3,4,7,14,28,56,112,116,0,0,0,0,0,0},
{9,1,2,4,5,10,14,28,56,112,117,0,0,0,0,0,0},
{9,1,2,4,6,12,24,28,56,112,118,0,0,0,0,0,0},
{9,1,2,4,6,7,14,28,56,112,119,0,0,0,0,0,0},
{8,1,2,4,8,16,24,48,96,120,0,0,0,0,0,0,0},
{9,1,2,4,8,16,24,48,96,120,121,0,0,0,0,0,0},
{9,1,2,4,8,16,24,48,96,120,122,0,0,0,0,0,0},
{9,1,2,3,6,12,24,48,96,120,123,0,0,0,0,0,0},
{9,1,2,4,8,16,24,48,96,120,124,0,0,0,0,0,0},
{9,1,2,4,5,10,20,40,80,120,125,0,0,0,0,0,0},
{9,1,2,4,6,12,24,48,96,120,126,0,0,0,0,0,0},
{10,1,2,4,6,12,24,48,96,120,126,127,0,0,0,0,0},
{7,1,2,4,8,16,32,64,128,0,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,128,129,0,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,128,130,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,130,131,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,128,132,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,132,133,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,132,134,0,0,0,0,0,0},
{9,1,2,3,6,12,15,30,60,120,135,0,0,0,0,0,0},
{8,1,2,4,8,16,32,64,128,136,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,136,137,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,136,138,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,136,138,139,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,136,140,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,136,140,141,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,136,140,142,0,0,0,0,0},
{10,1,2,3,5,10,20,40,80,120,140,143,0,0,0,0,0},
{8,1,2,4,8,16,32,64,128,144,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,144,145,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,144,146,0,0,0,0,0,0},
{9,1,2,3,6,12,24,48,96,144,147,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,144,148,0,0,0,0,0,0},
{9,1,2,4,5,9,18,36,72,144,149,0,0,0,0,0,0},
{9,1,2,4,6,12,24,48,96,144,150,0,0,0,0,0,0},
{10,1,2,4,6,12,24,48,96,144,150,151,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,144,152,0,0,0,0,0,0},
{9,1,2,4,8,9,18,36,72,144,153,0,0,0,0,0,0},
{9,1,2,4,8,10,18,36,72,144,154,0,0,0,0,0,0},
{10,1,2,4,8,10,18,36,72,144,154,155,0,0,0,0,0},
{9,1,2,4,8,12,24,48,96,144,156,0,0,0,0,0,0},
{10,1,2,4,8,12,24,48,96,144,156,157,0,0,0,0,0},
{10,1,2,4,8,12,24,48,96,144,156,158,0,0,0,0,0},
{10,1,2,3,6,12,24,48,96,144,156,159,0,0,0,0,0},
{8,1,2,4,8,16,32,64,128,160,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,160,161,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,160,162,0,0,0,0,0,0},
{9,1,2,3,5,10,20,40,80,160,163,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,160,164,0,0,0,0,0,0},
{9,1,2,4,5,10,20,40,80,160,165,0,0,0,0,0,0},
{9,1,2,4,6,10,20,40,80,160,166,0,0,0,0,0,0},
{10,1,2,4,6,10,20,40,80,160,166,167,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,160,168,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,160,168,169,0,0,0,0,0},
{9,1,2,4,8,10,20,40,80,160,170,0,0,0,0,0,0},
{10,1,2,4,8,10,20,40,80,160,170,171,0,0,0,0,0},
{9,1,2,4,8,12,20,40,80,160,172,0,0,0,0,0,0},
{10,1,2,4,8,12,20,40,80,160,172,173,0,0,0,0,0},
{10,1,2,4,8,12,20,40,80,160,172,174,0,0,0,0,0},
{10,1,2,3,5,10,20,40,43,86,172,175,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,160,176,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,160,176,177,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,160,176,178,0,0,0,0,0},
{10,1,2,3,5,10,20,22,44,88,176,179,0,0,0,0,0},
{9,1,2,4,8,16,20,40,80,160,180,0,0,0,0,0,0},
{10,1,2,4,8,16,20,40,80,160,180,181,0,0,0,0,0},
{10,1,2,4,8,16,20,40,80,160,180,182,0,0,0,0,0},
{10,1,2,3,5,10,20,40,80,160,180,183,0,0,0,0,0},
{9,1,2,4,8,16,24,40,80,160,184,0,0,0,0,0,0},
{10,1,2,4,8,16,24,40,80,160,184,185,0,0,0,0,0},
{10,1,2,4,8,16,24,40,80,160,184,186,0,0,0,0,0},
{10,1,2,3,5,10,20,23,46,92,184,187,0,0,0,0,0},
{10,1,2,4,8,16,24,40,80,160,184,188,0,0,0,0,0},
{10,1,2,3,5,10,20,23,46,92,184,189,0,0,0,0,0},
{10,1,2,4,6,10,20,40,46,92,184,190,0,0,0,0,0},
{11,1,2,4,6,10,20,40,46,92,184,190,191,0,0,0,0},
{8,1,2,4,8,16,32,64,128,192,0,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,192,193,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,192,194,0,0,0,0,0,0},
{9,1,2,3,6,12,24,48,96,192,195,0,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,192,196,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,192,196,197,0,0,0,0,0},
{9,1,2,4,6,12,24,48,96,192,198,0,0,0,0,0,0},
{10,1,2,4,6,12,24,48,96,192,198,199,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,192,200,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,192,200,201,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,192,200,202,0,0,0,0,0},
{10,1,2,3,5,10,20,40,80,160,200,203,0,0,0,0,0},
{9,1,2,4,8,12,24,48,96,192,204,0,0,0,0,0,0},
{10,1,2,4,8,12,24,48,96,192,204,205,0,0,0,0,0},
{10,1,2,4,8,12,24,48,96,192,204,206,0,0,0,0,0},
{10,1,2,3,6,12,24,48,96,192,204,207,0,0,0,0,0},
{9,1,2,4,8,16,32,64,128,192,208,0,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,192,208,209,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,192,208,210,0,0,0,0,0},
{10,1,2,3,6,12,24,26,52,104,208,211,0,0,0,0,0},
{10,1,2,4,8,16,32,64,128,192,208,212,0,0,0,0,0},
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{14,1,2,4,5,9,18,36,41,82,118,236,472,944,1888,1893,0},
{14,1,2,4,6,12,24,28,56,112,224,448,472,944,1888,1894,0},
{14,1,2,4,6,7,14,28,56,112,118,236,472,944,1888,1895,0},
{14,1,2,4,6,8,14,28,56,112,118,236,472,944,1888,1896,0},
{14,1,2,4,8,9,17,34,42,84,118,236,472,944,1888,1897,0},
{14,1,2,4,8,10,18,36,72,82,164,236,472,944,1888,1898,0},
{14,1,2,3,6,12,24,27,54,78,156,312,624,1248,1872,1899,0},
{14,1,2,4,8,12,24,48,56,112,224,448,896,944,1888,1900,0},
{14,1,2,4,6,7,13,26,52,59,118,236,472,944,1888,1901,0},
{14,1,2,4,8,12,14,28,56,112,224,236,472,944,1888,1902,0},
{15,1,2,4,8,12,14,28,56,112,224,236,472,944,1888,1902,1903},
{13,1,2,4,8,16,32,64,96,112,224,448,896,1792,1904,0,0},
{14,1,2,4,8,16,32,64,96,112,224,448,896,1792,1904,1905,0},
{14,1,2,4,8,16,32,64,96,112,224,448,896,1792,1904,1906,0},
{14,1,2,3,6,12,14,28,56,112,224,448,896,1792,1904,1907,0},
{14,1,2,3,4,7,14,28,56,112,224,448,896,1792,1904,1908,0},
{14,1,2,4,5,10,14,28,56,112,224,448,896,1792,1904,1909,0},
{14,1,2,4,6,12,24,28,56,112,224,448,896,1792,1904,1910,0},
{14,1,2,4,6,7,14,28,56,112,224,448,896,1792,1904,1911,0},
{14,1,2,4,6,8,14,28,56,112,224,448,896,1792,1904,1912,0},
{14,1,2,4,5,9,14,28,56,112,224,448,896,1792,1904,1913,0},
{14,1,2,4,8,10,20,28,56,112,224,448,896,1792,1904,1914,0},
{14,1,2,4,5,9,18,27,54,59,118,236,472,944,1888,1915,0},
{14,1,2,4,8,12,24,48,56,112,224,448,896,1792,1904,1916,0},
{14,1,2,4,8,9,18,27,45,90,117,234,468,936,1872,1917,0},
{14,1,2,4,8,12,14,28,56,112,224,448,896,1792,1904,1918,0},
{14,1,2,3,6,12,14,28,31,59,118,236,472,944,1888,1919,0},
{12,1,2,4,8,16,32,64,128,256,384,768,1536,1920,0,0,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1921,0,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1922,0,0},
{13,1,2,3,6,12,24,48,96,192,384,768,1536,1920,1923,0,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1924,0,0},
{13,1,2,4,5,10,20,40,80,160,320,640,1280,1920,1925,0,0},
{13,1,2,4,6,12,24,48,96,192,384,768,1536,1920,1926,0,0},
{14,1,2,4,6,12,24,48,96,192,384,768,1536,1920,1926,1927,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1928,0,0},
{13,1,2,3,6,9,15,30,60,120,240,480,960,1920,1929,0,0},
{13,1,2,4,8,10,20,40,80,160,320,640,1280,1920,1930,0,0},
{14,1,2,4,8,10,20,40,80,160,320,640,1280,1920,1930,1931,0},
{13,1,2,4,8,12,24,48,96,192,384,768,1536,1920,1932,0,0},
{14,1,2,4,8,12,24,48,96,192,384,768,1536,1920,1932,1933,0},
{14,1,2,4,8,12,24,48,96,192,384,768,1536,1920,1932,1934,0},
{13,1,2,3,6,12,15,30,60,120,240,480,960,1920,1935,0,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1936,0,0},
{14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1936,1937,0},
{13,1,2,4,6,12,18,30,60,120,240,480,960,1920,1938,0,0},
{14,1,2,4,6,12,18,30,60,120,240,480,960,1920,1938,1939,0},
{13,1,2,4,8,16,20,40,80,160,320,640,1280,1920,1940,0,0},
{14,1,2,4,8,16,20,40,80,160,320,640,1280,1920,1940,1941,0},
{14,1,2,4,8,16,20,40,80,160,320,640,1280,1920,1940,1942,0},
{14,1,2,3,5,10,20,40,80,160,320,640,1280,1920,1940,1943,0},
{13,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,0,0},
{14,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,1945,0},
{14,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,1946,0},
{14,1,2,3,6,12,24,48,96,192,384,768,1536,1920,1944,1947,0},
{14,1,2,4,8,16,24,48,96,192,384,768,1536,1920,1944,1948,0},
{14,1,2,4,5,9,18,36,72,144,216,432,864,1728,1944,1949,0},
{13,1,2,4,6,12,24,30,60,120,240,480,960,1920,1950,0,0},
{14,1,2,4,6,12,24,30,60,120,240,480,960,1920,1950,1951,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1952,0,0},
{14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1952,1953,0},
{14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1952,1954,0},
{14,1,2,3,6,12,24,48,96,98,196,392,488,976,1952,1955,0},
{13,1,2,4,8,12,24,36,60,120,240,480,960,1920,1956,0,0},
{14,1,2,4,8,12,24,36,60,120,240,480,960,1920,1956,1957,0},
{14,1,2,4,8,12,24,36,60,120,240,480,960,1920,1956,1958,0},
{14,1,2,3,6,12,24,36,60,120,240,480,960,1920,1956,1959,0},
{13,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,0,0},
{14,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,1961,0},
{14,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,1962,0},
{14,1,2,3,5,10,20,40,80,160,320,640,1280,1920,1960,1963,0},
{14,1,2,4,8,16,32,40,80,160,320,640,1280,1920,1960,1964,0},
{14,1,2,4,5,10,20,40,80,160,320,640,1280,1920,1960,1965,0},
{14,1,2,4,6,10,20,40,80,160,320,640,1280,1920,1960,1966,0},
{14,1,2,4,5,10,15,30,60,120,240,244,488,976,1952,1967,0},
{13,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,0,0},
{14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1969,0},
{14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1970,0},
{14,1,2,3,6,12,24,48,96,192,384,768,1536,1920,1968,1971,0},
{14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1972,0},
{14,1,2,4,5,10,20,40,80,160,164,328,656,1312,1968,1973,0},
{14,1,2,4,6,12,24,48,96,192,384,768,1536,1920,1968,1974,0},
{14,1,2,4,5,10,15,30,60,120,240,480,490,980,1960,1975,0},
{14,1,2,4,8,16,32,48,96,192,384,768,1536,1920,1968,1976,0},
{14,1,2,4,5,9,18,36,41,82,164,328,656,1312,1968,1977,0},
{14,1,2,4,8,10,20,40,80,160,320,328,656,1312,1968,1978,0},
{15,1,2,4,8,10,20,40,80,160,320,328,656,1312,1968,1978,1979},
{13,1,2,4,8,12,24,48,60,120,240,480,960,1920,1980,0,0},
{14,1,2,4,8,12,24,48,60,120,240,480,960,1920,1980,1981,0},
{14,1,2,4,8,12,24,48,60,120,240,480,960,1920,1980,1982,0},
{14,1,2,3,6,12,24,48,60,120,240,480,960,1920,1980,1983,0},
{13,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1984,0,0},
{14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1984,1985,0},
{14,1,2,4,8,16,32,64,128,256,384,768,1536,1920,1984,1986,0},
{14,1,2,3,6,12,24,48,50,100,200,248,496,992,1984,1987,0},
{14,1,2,3,4,7,14,28,31,62,124,248,496,992,1984,1988,0},
{14,1,2,4,5,10,20,40,80,84,168,248,496,992,1984,1989,0},
{14,1,2,4,6,12,24,48,96,100,200,400,496,992,1984,1990,0},
{14,1,2,4,6,7,14,28,56,62,124,248,496,992,1984,1991,0},
{13,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,0,0},
{14,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,1993,0},
{14,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,1994,0},
{14,1,2,3,6,12,24,48,72,120,240,480,960,1920,1992,1995,0},
{14,1,2,4,8,16,24,48,72,120,240,480,960,1920,1992,1996,0},
{14,1,2,3,5,10,20,40,80,83,166,332,664,1328,1992,1997,0},
{14,1,2,4,6,12,24,48,72,120,240,480,960,1920,1992,1998,0},
{14,1,2,4,5,10,15,30,60,120,124,248,496,992,1984,1999,0},
{13,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,0,0},
{14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2001,0},
{14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2002,0},
{14,1,2,3,5,10,20,40,80,160,320,640,1280,1920,2000,2003,0},
{14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2004,0},
{14,1,2,4,5,10,20,40,80,160,320,640,1280,1920,2000,2005,0},
{14,1,2,4,6,10,20,40,80,160,320,640,1280,1920,2000,2006,0},
{14,1,2,3,6,9,15,30,60,120,240,249,498,996,1992,2007,0},
{14,1,2,4,8,16,32,64,80,160,320,640,1280,1920,2000,2008,0},
{14,1,2,4,8,9,17,25,50,100,200,400,800,1600,2000,2009,0},
{14,1,2,4,8,10,20,40,80,160,320,640,1280,1920,2000,2010,0},
{14,1,2,4,8,9,18,27,54,62,124,248,496,992,1984,2011,0},
{14,1,2,4,8,12,20,40,80,160,320,640,1280,1920,2000,2012,0},
{14,1,2,4,8,12,13,25,50,100,200,400,800,1600,2000,2013,0},
{14,1,2,4,8,10,20,30,60,120,240,248,496,992,1984,2014,0},
{14,1,2,4,5,10,15,25,50,100,200,400,800,1600,2000,2015,0},
{13,1,2,4,8,16,32,64,96,192,384,768,1536,1920,2016,0,0},
{14,1,2,4,8,16,32,64,96,192,384,768,1536,1920,2016,2017,0},
{14,1,2,4,8,16,32,64,96,192,384,768,1536,1920,2016,2018,0},
{14,1,2,3,6,12,24,48,96,192,384,768,1536,1920,2016,2019,0},
{14,1,2,3,4,7,14,28,56,112,224,448,896,1792,2016,2020,0},
{14,1,2,4,5,10,14,28,56,112,224,448,896,1792,2016,2021,0},
{14,1,2,4,6,12,24,48,96,192,384,768,1536,1920,2016,2022,0},
{14,1,2,4,6,7,14,28,56,112,224,448,896,1792,2016,2023,0},
{14,1,2,4,6,8,14,28,56,112,224,448,896,1792,2016,2024,0},
{14,1,2,4,5,9,14,28,56,112,224,448,896,1792,2016,2025,0},
{14,1,2,4,8,10,20,28,56,112,224,448,896,1792,2016,2026,0},
{14,1,2,4,8,10,11,21,42,84,168,336,672,1344,2016,2027,0},
{14,1,2,3,6,9,12,21,42,84,168,336,672,1344,2016,2028,0},
{14,1,2,3,5,8,13,21,42,84,168,336,672,1344,2016,2029,0},
{14,1,2,4,8,12,14,28,56,112,224,448,896,1792,2016,2030,0},
{14,1,2,3,6,12,15,30,42,84,168,336,672,1344,2016,2031,0},
{14,1,2,4,8,12,16,28,56,112,224,448,896,1792,2016,2032,0},
{14,1,2,4,8,16,17,34,68,84,168,336,672,1344,2016,2033,0},
{14,1,2,4,8,10,18,28,56,112,224,448,896,1792,2016,2034,0},
{14,1,2,3,5,10,20,40,43,83,166,332,664,1328,1992,2035,0},
{14,1,2,4,8,16,20,40,56,112,224,448,896,1792,2016,2036,0},
{14,1,2,4,8,16,20,21,42,84,168,336,672,1344,2016,2037,0},
{14,1,2,4,8,16,20,22,42,84,168,336,672,1344,2016,2038,0},
{14,1,2,3,5,10,20,23,43,63,126,252,504,1008,2016,2039,0},
{13,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,0,0},
{14,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,2041,0},
{14,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,2042,0},
{14,1,2,3,6,12,24,48,96,120,240,480,960,1920,2040,2043,0},
{14,1,2,4,8,16,24,48,96,120,240,480,960,1920,2040,2044,0},
{14,1,2,4,5,10,20,40,80,120,240,480,960,1920,2040,2045,0},
{14,1,2,4,6,12,24,48,96,120,240,480,960,1920,2040,2046,0},
{15,1,2,4,6,12,24,48,96,120,240,480,960,1920,2040,2046,2047},
{11,1,2,4,8,16,32,64,128,256,512,1024,2048,0,0,0,0}};

#endif // ADDITIONCHAINS_H