34 lines
1.2 KiB
Python
34 lines
1.2 KiB
Python
#!/usr/bin/env python3
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TESTS = [
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[12, 3, 8],
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[2, 15, 17],
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[456, 6, 1296],
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[1234, 100, 9],
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[11223344, 1000000, 142857],
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[55667788, 10000000, 1000000007],
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[1357, 24682468, 999999999],
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[24680, 1357913579, 777777777],
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[998, 1000000000000, 999],
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[1234, 11111111111111, 30],
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[1, 222222222222222, 123456789],
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[2016, 666666666666666, 8888888888],
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[11223344, 555666777888999, 1357924680],
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[999999999999999967, 999999999999999877, 999999999999999989],
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[123456789123456789, 123456789123456789, 987654321123456789]
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]
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# Gọi l là "chiều dài" của x, l = int(log10(x) + 1) hay l = len(str(x))
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# Đặt l ** 10 = a, dễ thấy y = x * (a**(n-1) + a**(n-2) + ... + a + 1)
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# = x * (a**n - 1) / (a - 1)
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# y chia m bằng k dư q hay x * (a**n - 1) / (a - 1) = k * m + q
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# <=> x * (a**n - 1) = k * (a*m - a) + q * (a - 1)
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# <=> q = x * (a**n - 1) % (a*m - a) / (a - 1)
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with open('REMAINDER.TXT', 'w') as f:
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for case in TESTS:
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a = 10 ** len(str(case[0]))
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case[2] *= a - 1
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p = pow(a, case[1], case[2])
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f.write(str(case[0] * (p - 1) % case[2] // (a - 1)) + '\n')
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