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63 lines
1.5 KiB
C++
63 lines
1.5 KiB
C++
#include <iostream>
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#include <algorithm>
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#include <limits>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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int t;
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long long l;
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long long euler(long long x) {
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long long r = x;
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for (long long i = 2; i * i <= x; i++) {
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if (x % i == 0) {
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r = r / i * (i - 1);
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while (x % i == 0) x /= i;
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}
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}
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if (x > 1) r = r / x * (x - 1);
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return r;
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}
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long long binmul(long long a, long long b, long long m) {
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unsigned long long c =
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(unsigned long long)a * b -
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(unsigned long long)((long double)a / m * b + 0.5L) * m;
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if (c < m) return c;
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return c + m;
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}
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long long binpow(long long a, long long b, long long m) {
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a %= m;
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long long res = 1;
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while (b > 0) {
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if (b & 1) res = binmul(res, a, m);
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a = binmul(a, a, m);
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b >>= 1;
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}
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return res;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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while (cin >> l, l) {
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long long d = std::__gcd(l, 8ll);
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long long n = euler(9ll * l / d);
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long long ans = std::numeric_limits<long long>::max();
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for (long long i = 1; i * i <= n; i++) {
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if (n % i == 0) {
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if (binpow(10, i, 9ll * l / d) == 1) ans = std::min(ans, i);
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if (binpow(10, n / i, 9ll * l / d) == 1) ans = std::min(ans, n / i);
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}
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}
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cout << "Case " << ++t << ": " << (ans == std::numeric_limits<long long>::max() ? 0 : ans) << endl;
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}
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return 0;
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}
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