結果
| 問題 | No.2578 Jewelry Store |
| ユーザー |
 suisen
|
| 提出日時 | 2023-01-13 17:55:24 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 608 ms / 3,500 ms |
| コード長 | 5,646 bytes |
| コンパイル時間 | 1,473 ms |
| コンパイル使用メモリ | 118,296 KB |
| 最終ジャッジ日時 | 2025-02-10 01:54:23 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 54 |
ソースコード
#include <algorithm>#include <iostream>#include <random>#include <vector>#include <atcoder/modint>using mint = atcoder::modint998244353;namespace details {template <typename T>constexpr int floor_log2(T n) {int i = 0;while (n) n >>= 1, ++i;return i - 1;}constexpr bool miller_rabin(uint64_t n) {if (n <= 1) return false;uint64_t d = (n - 1) >> __builtin_ctzll(n - 1);if (n == 2 or n == 3 or n == 5 or n == 7) {return true;}if (n % 2 == 0 or n % 3 == 0 or n % 5 == 0 or n % 7 == 0) {return false;}for (uint64_t p : { 2U, 325U, 9375U, 28178U, 450775U, 9780504U, 1795265022U }) {p %= n;if (p == 0) {continue;}uint64_t y = 1;for (uint64_t d2 = d; d2; d2 >>= 1) {if (d2 & 1) {y = __uint128_t(y) * p % n;}p = __uint128_t(p) * p % n;}if (y == 1) {continue;}for (uint64_t t = d; y != n - 1; t <<= 1) {y = __uint128_t(y) * y % n;if (y == 1 or t == n - 1) {return false;}}}return true;}uint64_t pollard_rho(uint64_t n) {const uint64_t m = uint64_t(1) << (floor_log2(n) / 5);static std::mt19937_64 rng{ std::random_device{}() };std::uniform_int_distribution<uint64_t> dist(0, n - 1);while (true) {uint64_t c = dist(rng);auto f = [&](uint64_t x) -> uint64_t {return (__uint128_t(x) * x + c) % n;};uint64_t x, y = 2, ys, q = 1, g = 1;for (uint64_t r = 1; g == 1; r <<= 1) {x = y;for (uint64_t i = 0; i < r; ++i) {y = f(y);}for (uint64_t k = 0; k < r and g == 1; k += m) {ys = y;for (uint64_t i = 0; i < std::min(m, r - k); ++i) {y = f(y), q = __uint128_t(q) * (x > y ? x - y : y - x) % n;}g = std::gcd(q, n);}}if (g == n) {g = 1;while (g == 1) {ys = f(ys), g = std::gcd(x > ys ? x - ys : ys - x, n);}}if (g < n) {if (miller_rabin(g)) {return g;}if (uint64_t d = n / g; miller_rabin(d)) {return d;}return pollard_rho(g);}}}}std::vector<std::pair<uint64_t, int>> factorize(uint64_t n) {std::vector<std::pair<uint64_t, int>> res;if ((n & 1) == 0) {int q = 0;do ++q, n >>= 1; while ((n & 1) == 0);res.emplace_back(2, q);}for (uint64_t p = 3; p * p <= n; p += 2) {if (p >= 101 and n >= 1 << 20) {while (n > 1) {if (details::miller_rabin(n)) {res.emplace_back(std::exchange(n, 1), 1);} else {p = details::pollard_rho(n);int q = 0;do ++q, n /= p; while (n % p == 0);res.emplace_back(p, q);}}break;}if (n % p == 0) {int q = 0;do ++q, n /= p; while (n % p == 0);res.emplace_back(p, q);}}if (n > 1) {res.emplace_back(n, 1);}return res;}std::vector<uint64_t> prime_factors(uint64_t m) {std::vector<uint64_t> res;for (const auto &prime_power : factorize(m)) {res.push_back(prime_power.first);}return res;}mint solve(uint32_t n, uint64_t m, std::vector<uint64_t> pf, std::vector<uint64_t> a, std::vector<uint32_t> w) {const uint32_t k = pf.size();std::vector<mint> zeta(1 << k, 1);for (uint32_t i = 0; i < n; ++i) if (m % a[i] == 0) {uint32_t t = 0;for (uint32_t j = 0; j < k; ++j) {uint64_t p = pf[j];if ((m / p) % a[i] == 0) {t |= 1 << j;}}zeta[t] *= 1 + w[i];}// Zeta transformfor (uint32_t block = 1; block < zeta.size(); block *= 2) {for (uint32_t offset = 0; offset < zeta.size(); offset += 2 * block) {for (uint32_t i = 0; i < block; ++i) {zeta[offset + i] *= zeta[offset + block + i];}}}mint ans = 0;for (uint32_t s = 0; s < zeta.size(); ++s) {if (__builtin_popcount(s) & 1) {ans -= zeta[s];} else {ans += zeta[s];}}return ans - (m == 1);}int main() {std::ios::sync_with_stdio(false);std::cin.tie(nullptr);uint32_t t;uint64_t m;std::cin >> t >> m;std::vector<uint64_t> pf = prime_factors(m);for (uint32_t testcase = 0; testcase < t; ++testcase) {uint32_t n;std::cin >> n;uint32_t x0, c, d;std::cin >> x0 >> c >> d;std::vector<uint32_t> w(n);w[0] = x0;for (uint32_t i = 1; i < n; ++i) {w[i] = (c * mint(w[i - 1]) + d).val();}std::vector<uint64_t> a(n);for (auto& e : a) std::cin >> e;std::cout << solve(n, m, pf, a, w).val() << '\n';}return 0;}