結果
問題 | No.2959 Dolls' Tea Party |
ユーザー |
👑 ![]() |
提出日時 | 2024-11-08 22:25:38 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 967 ms / 3,000 ms |
コード長 | 9,881 bytes |
コンパイル時間 | 4,606 ms |
コンパイル使用メモリ | 254,588 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-11-08 22:26:00 |
合計ジャッジ時間 | 21,517 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 33 |
ソースコード
#line 1 "a.cpp"#include <bits/stdc++.h>using namespace std;using ll=long long;using ld=long double;const ll ILL=2167167167167167167;const int INF=2100000000;#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)#define all(p) p.begin(),p.end()template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}template<class T> bool chmin(T &a,T b){if(a>b){a=b;return 1;}else return 0;}template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}bool yneos(bool a,bool upp=0){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}template<class T> void vec_out(vector<T> &p,int ty=0){if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}#include <atcoder/modint>using mint = atcoder::modint998244353;#line 3 "/Users/Shared/po167_library/fps/FPS_inv.hpp"#include <atcoder/convolution>namespace po167{// return 1 / ftemplate <class T>std::vector<T> FPS_inv(std::vector<T> f, int len = -1){if (len == -1) len = f.size();assert(f[0] != 0);std::vector<T> g = {1 / f[0]};int s = 1;while(s < len){// g = 2g_s - f(g_s)^2 (mod x ^ (2 * s))// g = g - (fg - 1)g// (fg - 1) = 0 (mod x ^ (s))std::vector<T> n_g(s * 2, 0);std::vector<T> f_s(s * 2, 0);g.resize(s * 2);for (int i = 0; i < s * 2; i++){if (int(f.size()) > i) f_s[i] = f[i];n_g[i] = g[i];}atcoder::internal::butterfly(g);atcoder::internal::butterfly(f_s);for (int i = 0; i < s * 2; i++){f_s[i] *= g[i];}atcoder::internal::butterfly_inv(f_s);T iz = 1 / (T)(s * 2);for (int i = s; i < s * 2; i++){f_s[i] *= iz;}for (int i = 0; i < s; i++){f_s[i] = 0;}atcoder::internal::butterfly(f_s);for (int i = 0; i < s * 2; i++){f_s[i] *= g[i];}atcoder::internal::butterfly_inv(f_s);for (int i = s; i < s * 2; i++){n_g[i] -= f_s[i] * iz;}std::swap(n_g, g);s *= 2;}g.resize(len);return g;}}#line 2 "/Users/Shared/po167_library/math/Binomial.hpp"#line 5 "/Users/Shared/po167_library/math/Binomial.hpp"namespace po167{template<class T>struct Binomial{std::vector<T> fact_vec, fact_inv_vec;void extend(int m = -1){int n = fact_vec.size();if (m == -1) m = n * 2;if (n >= m) return;fact_vec.resize(m);fact_inv_vec.resize(m);for (int i = n; i < m; i++){fact_vec[i] = fact_vec[i - 1] * T(i);}fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1];for (int i = m - 1; i > n; i--){fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i);}}Binomial(int MAX = 0){fact_vec.resize(1, T(1));fact_inv_vec.resize(1, T(1));extend(MAX + 1);}T fact(int i){if (i < 0) return 0;while (int(fact_vec.size()) <= i) extend();return fact_vec[i];}T invfact(int i){if (i < 0) return 0;while (int(fact_inv_vec.size()) <= i) extend();return fact_inv_vec[i];}T C(int a, int b){if (a < b || b < 0) return 0;return fact(a) * invfact(b) * invfact(a - b);}T invC(int a, int b){if (a < b || b < 0) return 0;return fact(b) * fact(a - b) *invfact(a);}T P(int a, int b){if (a < b || b < 0) return 0;return fact(a) * invfact(a - b);}T inv(int a){if (a < 0) return inv(-a) * T(-1);if (a == 0) return 1;return fact(a - 1) * invfact(a);}T Catalan(int n){if (n < 0) return 0;return fact(2 * n) * invfact(n + 1) * invfact(n);}T narayana(int n, int k){if (n <= 0 || n < k || k < 1) return 0;return C(n, k) * C(n, k - 1) * inv(n);}T Catalan_pow(int n,int d){if (n < 0 || d < 0) return 0;if (d == 0){if (n == 0) return 1;return 0;}return T(d) * inv(d + n) * C(2 * n + d - 1, n);}// retrun [x^a] 1/(1-x)^bT ruiseki(int a,int b){if (a < 0 || b < 0) return 0;if (a == 0){return 1;}return C(a + b - 1, b - 1);}// (a, b) -> (c, d)// always x + e >= yT mirror(int a, int b, int c, int d, int e = 0){if (a + e < b || c + e < d) return 0;if (a > c || b > d) return 0;a += e;c += e;return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1);}// return sum_{i = 0, ... , a} sum_{j = 0, ... , b} C(i + j, i)// return C(a + b + 2, a + 1) - 1;T gird_sum(int a, int b){if (a < 0 || b < 0) return 0;return C(a + b + 2, a + 1) - 1;}// return sum_{i = a, ..., b - 1} sum_{j = c, ... , d - 1} C(i + j, i)// AGC 018 ET gird_sum_2(int a, int b, int c, int d){if (a >= b || c >= d) return 0;a--, b--, c--, d--;return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d);}};}#line 3 "/Users/Shared/po167_library/fps/FPS_differetial.hpp"namespace po167{// return f'template <class T>std::vector<T> FPS_differential(std::vector<T> f){if (f.empty()) return f;for (int i = 0; i < (int)f.size() - 1; i++){f[i] = f[i + 1] * (T)(i + 1);}f.pop_back();return f;}}#line 3 "/Users/Shared/po167_library/fps/FPS_integral.hpp"namespace po167{template <class T>std::vector<T> FPS_integral(std::vector<T> f){if (f.empty()) return f;std::vector<T> num_inv((int)f.size() + 1);num_inv[0] = 1;num_inv[1] = 1;auto m = T::mod();for (int i = 2; i <= (int)f.size(); i++){num_inv[i] = (0 - num_inv[m % i]) * (T)(m / i);}f.reserve((int)f.size() + 1);f.push_back(0);for (int i = (int)f.size() - 1; i > 0; i--){f[i] = f[i - 1] * num_inv[i];}f[0] = 0;return f;}}#line 5 "/Users/Shared/po167_library/fps/FPS_log.hpp"namespace po167{template<class T>std::vector<T> FPS_log(std::vector<T> f, int len = -1){if (len == -1) len = f.size();if (len == 0) return {};if (len == 1) return {T(0)};assert(!f.empty() && f[0] == 1);std::vector<T> res = atcoder::convolution(FPS_differential(f), FPS_inv(f, len));res.resize(len - 1);return FPS_integral(res);}}#line 4 "/Users/Shared/po167_library/fps/FPS_cyclic_convolution.hpp"namespace po167{// |f| = |g| = 2 ^ ntemplate<class T>std::vector<T> FPS_cyclic_convolution(std::vector<T> f, std::vector<T> g){atcoder::internal::butterfly(f);atcoder::internal::butterfly(g);for (int i = 0; i < (int)f.size(); i++) f[i] *= g[i];atcoder::internal::butterfly_inv(f);T iz = (T)(1) / (T)(f.size());for (int i = 0; i < (int)f.size(); i++) f[i] *= iz;return f;}}#line 8 "/Users/Shared/po167_library/fps/FPS_exp.hpp"namespace po167{template<class T>std::vector<T> FPS_exp(std::vector<T> f, int len = -1){if (len == -1) len = f.size();if (len == 0) return {};if (len == 1) return {T(1)};assert(!f.empty() && f[0] == 0);int s = 1;// simplestd::vector<T> g = {T(1)};while (s < len){// g' / g// A * Bstd::vector<T> A = g, B = g;A = FPS_differential(A);B = FPS_inv(B, 2 * s);A.resize(2 * s);A = FPS_cyclic_convolution(A, B);A.pop_back();A = FPS_integral(A);for (int i = 0; i < s; i++) A[i] = 0;for (int i = s; i < s * 2; i++) A[i] = (i < (int)f.size() ? f[i] : 0) - A[i];// g_hat = g (1 - g + f)// g += B = g * Ag.resize(2 * s);B = FPS_cyclic_convolution(A, g);for (int i = s; i < s * 2; i++) g[i] = B[i];s *= 2;}g.resize(len);return g;}}#line 31 "a.cpp"void solve();// CYAN / FREDERICint main() {ios::sync_with_stdio(false);cin.tie(nullptr);int t = 1;// cin >> t;rep(i, 0, t) solve();}void solve(){int N, K;cin >> N >> K;vector<mint> C(K + 1);rep(i, 0, K){C[gcd(i, K)] += 1;}vector<int> A(N);rep(i, 0, N) cin >> A[i];mint ans = 0;po167::Binomial<mint> table;rep(len, 0, K + 1) if (C[len].val() != 0){vector<ll> D(len + 1);rep(i, 0, N){D[min(len, A[i] / (K / len))]++;}vector<mint> dp(len + 1);vector<mint> base(len + 1);rep(i, 0, len + 1){base[i] = table.invfact(i);if (D[i] != 0){auto tmp = po167::FPS_log(base);rep(j, 0, len + 1) dp[j] += tmp[j] * D[i];}}dp = po167::FPS_exp(dp);ans += dp.back() * table.fact(len) * C[len];}ans /= K;cout << ans.val() << "\n";}