#1120995 (C++17) No.3273 Exactly One Match

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結果

問題	No.3273 Exactly One Match
ユーザー	👑 potato167
提出日時	2025-09-13 03:03:53
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	1,427 ms / 4,000 ms
コード長	13,766 bytes
コンパイル時間	4,698 ms
コンパイル使用メモリ	246,876 KB
実行使用メモリ	62,872 KB
最終ジャッジ日時	2025-09-13 03:04:12
合計ジャッジ時間	17,826 ms
ジャッジサーバーID （参考情報）	judge3 / judge1
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 * 26
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ソースコード

raw source code
//#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 "po167_library/fps/FPS_pow.hpp"
//#include "po167_library/math/Binomial.hpp"
//using mint = atcoder::modint998244353;
//
//void solve();
//// POP'N ROLL MUSIC / TOMOO
//int main() {
//    ios::sync_with_stdio(false);
//    cin.tie(nullptr);
//
//    int t = 1;
//    // cin >> t;
//    rep(i, 0, t) solve();
//}
//
//void solve(){
//    int N;
//    ll K;
//    cin >> N >> K;
//    po167::Binomial<mint> table(N);
//    vector<mint> f(N + 1), g(N + 1);
//    rep(i, 0, N + 1){
//        f[i] = table.invfact(i);
//        f[i] *= ((mint)(N - i)).pow(i);
//        if (i){
//            g[i] = table.invfact(i);
//            g[i] *= ((mint)(N - i)).pow(i - 1);
//            g[i] *= i;
//            g[i] *= i;
//        }
//    }
//    f = po167::FPS_pow(f, K - 1);
//    f = atcoder::convolution(f, g);
//    mint ans = f[N];
//    ans *= table.fact(N);
//    ans *= K;
//    cout << ans.val() << "\n";
//}
///*
// * C[i] = a であるような i が K 個あるとする。
// * 被りなし (N - K)^{K}
// * 1 つ被り (N - K)^{K - 1} K^{2}
// * 思ったより簡単だった。。、
// */
#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;}

#line 2 "/Users/Shared/po167_library/fps/FPS_pow.hpp"

#line 4 "/Users/Shared/po167_library/fps/FPS_pow.hpp"
#include <atcoder/convolution>

#line 4 "/Users/Shared/po167_library/fps/FPS_cyclic_convolution.hpp"

namespace po167{
// |f| = |g| = 2 ^ n
template<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 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 4 "/Users/Shared/po167_library/fps/FPS_inv.hpp"

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 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;
    // simple
    std::vector<T> g = {T(1)};
    while (s < len){
        // g' / g
        // A * B
        std::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 * A
        g.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 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 8 "/Users/Shared/po167_library/fps/FPS_pow.hpp"

namespace po167{
template<class T>
std::vector<T> FPS_pow(std::vector<T> f,long long M, int len = -1){
    if (len == -1) len = f.size();
    std::vector<T> res(len, 0);
    if (M == 0){
        res[0] = 1;
        return res;
    }
    for (int i = 0; i < (int)f.size(); i++){
        if (f[i] == 0) continue;
        if (i > (len - 1) / M) break;
        std::vector<T> g((int)f.size() - i);
        T v = (T)(1) / (T)(f[i]);
        for (int j = i; j < (int)f.size(); j++){
            g[j - i] = f[j] * v;
        }
        long long zero = i * M;
        if (i) len -= i * M;
        g = FPS_log(g, len);
        for (T &x : g) x *= M;
        g = FPS_exp(g, len);
        v = (T)(1) / v;
        T c = 1;
        while (M){
            if (M & 1) c = c * v;
            v = v * v;
            M >>= 1;
        }
        for (int i = 0; i < len; i++) res[i + zero] = g[i] * c;
        return res;
    }
    return res;
}
}
#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)^b
    T 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 >= y
    T 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 E
    T 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);
    }

    // the number of diagonal dissections of a convex n-gon into k+1 regions.
    // OEIS A033282
    // AGC065D
    T diagonal(int n, int k){
        if (n <= 2 || n - 3 < k || k < 0) return 0;
        return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1);
    }
};
}
#line 27 "g.cpp"
using mint = atcoder::modint998244353;

void solve();
// POP'N ROLL MUSIC / TOMOO
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
    // cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    int N;
    ll K;
    cin >> N >> K;
    po167::Binomial<mint> table(N);
    vector<mint> f(N + 1), g(N + 1);
    rep(i, 0, N + 1){
        f[i] = table.invfact(i);
        f[i] *= ((mint)(N - i)).pow(i);
        if (i){
            g[i] = table.invfact(i);
            g[i] *= ((mint)(N - i)).pow(i - 1);
            g[i] *= i;
            g[i] *= i;
        }
    }
    f = po167::FPS_pow(f, K - 1);
    mint ans = 0;
    rep(i, 0, N + 1) ans += f[i] * g[N - i];
    ans *= table.fact(N);
    ans *= K;
    cout << ans.val() << "\n";
}
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結果

ソースコード
