結果
問題 | No.3095 Many Min Problems |
ユーザー |
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提出日時 | 2025-04-06 15:47:38 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 311 ms / 2,000 ms |
コード長 | 5,875 bytes |
コンパイル時間 | 3,795 ms |
コンパイル使用メモリ | 239,884 KB |
実行使用メモリ | 30,080 KB |
最終ジャッジ日時 | 2025-04-06 15:47:48 |
合計ジャッジ時間 | 9,616 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#line 1 "g.cpp" #include <bits/stdc++.h> using namespace std; using ll=long long; 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> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template<class T> int 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(b<a){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=false){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;} template<class T> T square(T a){return a * a;} #include <atcoder/modint> using mint = atcoder::modint998244353; #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 3 "/Users/Shared/po167_library/fps/FPS_inv.hpp" #include <atcoder/convolution> namespace po167{ // return 1 / f template <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 6 "/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_Product_Sequence.hpp" namespace po167{ template<class T> std::vector<T> FPS_Product_Sequence(std::vector<std::vector<T>> f){ if (f.empty()) return {1}; auto op = [&](auto self,int l, int r) -> std::vector<T> { if (l + 1 == r) return f[l]; int m = (l + r) / 2; return atcoder::convolution(self(self, l, m), self(self, m, r)); }; return op(op, 0, f.size()); } } #line 4 "/Users/Shared/po167_library/fps/FPS_sum_of_power.hpp" namespace po167{ template<class T> std::vector<T> FPS_sum_of_power(std::vector<T> A, int M){ std::vector<std::vector<T>> B(A.size()); for (int i = 0; i < (int)(A.size()); i++){ B[i] = {1, - A[i]}; } auto C = FPS_Product_Sequence(B); C = FPS_log(C, M + 1); std::vector<T> res(M + 1); res[0] = (int)A.size(); for (int i = 0; i < M; i++){ res[i + 1] = C[i + 1] * -1 * (i + 1); } return res; } } #line 29 "g.cpp" void solve(); // CITRUS CURIO CITY / FREDERIC int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t = 1; // cin >> t; rep(i, 0, t) solve(); } void solve(){ int N, M; cin >> N >> M; vector<mint> A(M); rep(i, 0, M) A[i] = i + 1; auto tmp = po167::FPS_sum_of_power(A, N + 1); mint ans = 0; mint pw = 1; for (int i = N; i >= 1; i --){ ans += pw * tmp[i]; pw *= M; } cout << ans.val() << "\n"; }