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cdef extern from "limits.h":
unsigned long ULONG_MAX
def _comb_int(N, k):
# Fast path with machine integers
try:
r = _comb_int_long(N, k)
if r != 0:
return r
except (OverflowError, TypeError):
pass
# Fallback
N = int(N)
k = int(k)
if k > N or N < 0 or k < 0:
return 0
M = N + 1
nterms = min(k, N - k)
numerator = 1
denominator = 1
for j in xrange(1, nterms + 1):
numerator *= M - j
denominator *= j
return numerator // denominator
cdef unsigned long _comb_int_long(unsigned long N, unsigned long k):
"""
Compute binom(N, k) for integers.
Returns 0 if error/overflow encountered.
"""
cdef unsigned long val, j, M, nterms
if k > N or N == ULONG_MAX:
return 0
M = N + 1
nterms = min(k, N - k)
val = 1
for j in xrange(1, nterms + 1):
# Overflow check
if val > ULONG_MAX // (M - j):
return 0
val *= M - j
val //= j
return val
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