結果
問題 | No.2576 LCM Pattern |
ユーザー |
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提出日時 | 2023-12-06 14:16:24 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 5 ms / 2,000 ms |
コード長 | 7,308 bytes |
コンパイル時間 | 4,983 ms |
コンパイル使用メモリ | 271,804 KB |
最終ジャッジ日時 | 2025-02-18 08:29:13 |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 23 |
ソースコード
#include <bits/stdc++.h>using namespace std;using ll = long long;using ld = long double;using ull = unsigned long long;using pll = pair<ll, ll>;using tlll = tuple<ll, ll, ll>;constexpr ll INF = 1LL << 60;template<class T> bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;}template<class T> bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;}ll safemod(ll A, ll M) {ll res = A % M; if (res < 0) res += M; return res;}ll divfloor(ll A, ll B) {if (B < 0) A = -A, B = -B; return (A - safemod(A, B)) / B;}ll divceil(ll A, ll B) {if (B < 0) A = -A, B = -B; return divfloor(A + B - 1, B);}ll pow_ll(ll A, ll B) {if (A == 0 || A == 1) {return A;} if (A == -1) {return B & 1 ? -1 : 1;} ll res = 1; for (int i = 0; i < B; i++) {res *= A;}return res;}ll mul_limited(ll A, ll B, ll M = INF) { return B == 0 ? 0 : A > M / B ? M : A * B; }ll pow_limited(ll A, ll B, ll M = INF) { if (A == 0 || A == 1) {return A;} ll res = 1; for (int i = 0; i < B; i++) {if (res > M / A) return M; res *=A;} return res;}template<class T> void unique(vector<T> &V) {V.erase(unique(V.begin(), V.end()), V.end());}template<class T> void sortunique(vector<T> &V) {sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end());}#define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false)template<class T> void printvec(const vector<T> &V) {int _n = V.size(); for (int i = 0; i < _n; i++) cout << V[i] << (i == _n - 1 ? "" : " ");cout <<'\n';}template<class T> void printvect(const vector<T> &V) {for (auto v : V) cout << v << '\n';}template<class T> void printvec2(const vector<vector<T>> &V) {for (auto &v : V) printvec(v);}//*#include <atcoder/all>using namespace atcoder;using mint = modint998244353;//using mint = modint1000000007;//using mint = modint;//*/bool isprime(ll n){if (n == 1)return false;const vector<ll> as = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};const vector<ll> ps = {2, 3, 5, 13, 19, 73, 193, 407521, 299210837};for (auto p : ps){if (n == p)return true;if (n % p == 0)return false;}ll d = n - 1;int s = 0;while (d % 2 == 0)d /= 2, s++;for (auto a : as){ll a0 = 1;for (ll d2 = d, tmp = a; d2 > 0; d2 /= 2, tmp = __int128_t(tmp) * tmp % n){if (d2 % 2 == 1)a0 = __int128_t(a0) * tmp % n;}if (a0 == 1 || a0 == n - 1)continue;for (int r = 1; r <= s; r++){if (r == s)return false;a0 = __int128_t(a0) * a0 % n;if (a0 == n - 1)break;}}return true;}ll getprimefactor(ll n){if (isprime(n))return n;int m = pow(n, .125);for (int c = 1; c < 100; c++){auto f = [&](ll a) -> ll{ return (__int128_t(a) * a + c) % n; };ll x = 2, y = 2, prod = 1, g = 1;while (g == 1){for (int i = 0; i < m; i++){x = f(x), y = f(f(y));prod = __int128_t(prod) * (x - y) % n;}g = gcd(prod, n);}if (g == n)continue;return getprimefactor(g);}assert(false);}vector<ll> factorize_fast(ll n){vector<ll> res;for (int p = 2; p < 100; p++){while (n % p == 0){n /= p;res.emplace_back(p);}}while (n > 1){ll p = getprimefactor(n);n /= p;res.emplace_back(p);}sort(res.begin(), res.end());return res;}vector<pll> to_vpll(const vector<ll> &ps){vector<pll> pes;for (auto p : ps){if (pes.empty() || pes.back().first != p)pes.emplace_back(make_pair(p, 1));elsepes.back().second++;}return pes;}vector<ll> divisors(const vector<pll> &pes){if (pes.empty())return {1};vector<ll> es(pes.size(), 0);auto next_es = [&]() -> bool{es[0]++;for (int i = 0; i < (int)es.size(); i++){if (es[i] <= pes[i].second)break;if (i == (int)es.size() - 1)return false;es[i] = 0;es[i + 1]++;}return true;};vector<ll> ds;do{ll d = 1;for (int i = 0; i < (int)es.size(); i++)d *= pow_ll(pes[i].first, es[i]);ds.emplace_back(d);} while (next_es());sort(ds.begin(), ds.end());return ds;}// https://nyaannyaan.github.io/library/multiplicative-function/divisor-multiple-transform.hpp.htmlstruct ZetaMobiusDivisorMultiple{ll n;vector<ll> ds, ps;ZetaMobiusDivisorMultiple() {}ZetaMobiusDivisorMultiple(ll n) : n(n){/* 通常for (ll d = 1; d * d <= n; d++){if (n % d == 0){ds.emplace_back(d);if (d * d != n)ds.emplace_back(n / d);}}sort(ds.begin(), ds.end());for (ll p = 2; p * p <= n; p++){if (n % p == 0){ps.emplace_back(p);while (n % p == 0)n /= p;}}if (n != 1)ps.emplace_back(n);//*///* 高速素因数分解に基づいた方法ps = factorize_fast(n);ds = divisors(to_vpll(ps));unique(ps);//*/}// d から f(d) を計算する関数を受け取って、実際に全部の d について計算した map を返すtemplate<class T>map<ll, T> func_to_map(const function<T(ll)> &f) const{map<ll, T> res;for (auto d : ds)res[d] = f(d);return res;}// ζa(n) = Σ{d | n} a(d)template<class T>map<ll, T> zeta_divisor(const map<ll, T> &A) const{map<ll, T> B(A);for (auto &p : ps){for (auto &d : ds){if (d > n / p)break;if (n % (d * p) == 0)B[d * p] += B[d];}}return B;}// μ は ζ の逆変換// μa(n) = Σ{d | n} μ(n/d)a(d) cf. メビウスの反転公式template<class T>map<ll, T> mobius_divisor(const map<ll, T> &A) const{map<ll, T> B(A);for (auto &p : ps){for (int i = (int)ds.size() - 1; i >= 0; i--){ll d = ds[i];if (d > n / p)continue;if (n % (d * p) == 0)B[d * p] -= B[d];}}return B;}// ζ'a(n) = Σ{n | m} a(m)template<class T>map<ll, T> zeta_multiple(const map<ll, T> &A) const{map<ll, T> B(A);for (auto &p : ps){for (int i = (int)ds.size() - 1; i >= 0; i--){ll d = ds[i];if (d > n / p)continue;if (n % (d * p) == 0)B[d] += B[d * p];}}return B;}// μ' は ζ' の逆変換// μ'a(n) = Σ{n | m} μ(m/n)g(m)template<class T>map<ll, T> mobius_multiple(const map<ll, T> &A) const{map<ll, T> B(A);for (auto &p : ps){for (auto &d : ds){if (d > n / p)break;if (n % (d * p) == 0)B[d] -= B[d * p];}}return B;}};int main(){ll N, M;cin >> N >> M;ZetaMobiusDivisorMultiple zmdm(M);map<ll, mint> sigma = zmdm.zeta_divisor(zmdm.func_to_map<mint>([&](ll) -> mint{ return 1; }));map<ll, mint> res = zmdm.mobius_divisor(zmdm.func_to_map<mint>([&](ll d) -> mint{ return sigma[d].pow(N); }));mint ans = res[M];cout << ans.val() << endl;}