結果
問題 | No.2066 Simple Math ! |
ユーザー |
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提出日時 | 2022-09-02 22:12:32 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 155 ms / 2,000 ms |
コード長 | 2,559 bytes |
コンパイル時間 | 1,494 ms |
コンパイル使用メモリ | 168,388 KB |
実行使用メモリ | 6,820 KB |
最終ジャッジ日時 | 2024-11-16 03:51:47 |
合計ジャッジ時間 | 5,995 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 31 |
ソースコード
#include <bits/stdc++.h>int ri() {int n;scanf("%d", &n);return n;}// @param n `n < 2^32`// @param m `1 <= m < 2^32`// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}// @param m `1 <= m`// @return x mod mconstexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}long long floor_sum(long long n, long long m, long long a, long long b) {assert(0 <= n && n < (1LL << 32));assert(1 <= m && m < (1LL << 32));unsigned long long ans = 0;if (a < 0) {unsigned long long a2 = safe_mod(a, m);ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);a = a2;}if (b < 0) {unsigned long long b2 = safe_mod(b, m);ans -= 1ULL * n * ((b2 - b) / m);b = b2;}return ans + floor_sum_unsigned(n, m, a, b);}int gcd(int a, int b) {while (a && b) {if (a > b) a %= b;else b %= a;}return a + b;}int64_t solve(int p, int q, int k) {int g = gcd(p, q);p /= g;q /= g;int64_t lcm = (int64_t) p * q;int64_t lcm_cnt = floor_sum(p, p, q, p + q - 1);// std::cerr << lcm_cnt << std::endl;if (k <= lcm_cnt) {int64_t l = -1;int64_t r = lcm;while (r - l > 1) {int64_t m = l + ((r - l) >> 1);uint64_t t0 = m / p;uint64_t t1 = m / q;if (t0 * t1 / t0 != t1 || t0 * t1 >= 1000000000000) {r = m;continue;}int64_t s = m / p;int64_t cur = floor_sum(s + 1, q, p, m - s * p) + s;// std::cerr << m << " " << cur << std::endl;if (cur < k) l = m;else r = m;}return r * g;} else {k -= lcm_cnt;return (lcm + k) * g;}}int main() {int t = ri();for (int i = 0; i < t; i++) {int p = ri();int q = ri();int k = ri();printf("%" PRId64 "\n", solve(p, q, k));}return 0;}