42 lines
748 B
Python
42 lines
748 B
Python
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#!/usr/bin/env python3
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from math import log
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digs = 5
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mask = 10**digs
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sieve = [1] * mask
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for n in range(1, mask):
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if n%2 and n%5:
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sieve[n] = (sieve[n-1] * n) % mask
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else:
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sieve[n] = sieve[n-1]
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def numf(n, N):
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return sum(N // (n**pw) for pw in range(1, int(log(N) / log(n))+1))
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def numof2(N):
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return numf(2, N) - numf(5, N)
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def roots(N):
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a = 1
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while a <= N:
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b = 1
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while a * b <= N:
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yield a * b
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b *= 2
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a *= 5
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def main(N):
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r = 1
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p = sieve[-1]
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for root in roots(N):
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d = N // root
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r *= pow(p, d // mask, mask)
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r *= sieve[d % mask]
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r %= mask
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r *= pow(2, numof2(N), mask)
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return r % mask
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print(main(10**12))
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