結果

問題 No.3095 Many Min Problems
コンテスト
ユーザー 👑 potato167
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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";
}
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