#1104921 (C++17) No.1614 Majority Painting on Tree

• 問題: No.1614 Majority Painting on Tree
• ユーザー: 👑 potato167
• 提出日時: 2025-07-15 18:24:48
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 584 ms / 5,000 ms
• コード長: 9,235 bytes
• コンパイル時間: 2,336 ms
• コンパイル使用メモリ: 207,620 KB
• 実行使用メモリ: 7,716 KB
• 最終ジャッジ日時: 2025-07-15 18:25:03
• 合計ジャッジ時間: 12,804 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 45

ソースコード

//#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;
//#include "po167_library/math/Binomial.hpp"
//
//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, C;
//    cin >> N >> C;
//    vector<int> deg(N);
//    rep(i, 0, N * 2 - 2){
//        int a;
//        cin >> a;
//        a--;
//        deg[a]++;
//    }
//    vector<mint> dp(C + 1);
//    po167::Binomial<mint> table;
//    rep(c, 1, C + 1){
//        vector<mint> p(N + 1, 1), q(N + 1, 1);
//        rep(i, 0, N) p[i + 1] = p[i] * c;
//        rep(i, 0, N) q[i + 1] = q[i] * (c - 1);
//        mint tmp = p[deg[0]];
//        rep(i, 1, (deg[0] - 1) / 2 + 1){
//            tmp -= table.C(deg[0], i) * q[i] * c;
//        }
//        dp[c] = tmp;
//        rep(i, 1, N){
//            // cout << c << " : " << dp[c].val() << "\n";
//            tmp = p[deg[i] - 1];
//            rep(j, 1, (deg[i] - 1) / 2 + 1){
//                tmp -= table.C(deg[i], j) * q[j];
//            }
//            dp[c] *= tmp;
//        }
//    }
//    mint ans = 0;
//    rep(i, 1, C + 1){
//        // cout << i << " " << dp[i].val() << "\n";
//        ans += dp[i] * table.C(C, i) * ((C - i) & 1 ? -1 : 1);
//    }
//    cout << ans.val() << "\n";
//}
#line 1 "e.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 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 28 "e.cpp"

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, C;
    cin >> N >> C;
    vector<int> deg(N);
    rep(i, 0, N * 2 - 2){
        int a;
        cin >> a;
        a--;
        deg[a]++;
    }
    vector<mint> dp(C + 1);
    po167::Binomial<mint> table;
    rep(c, 1, C + 1){
        vector<mint> p(N + 1, 1), q(N + 1, 1);
        rep(i, 0, N) p[i + 1] = p[i] * c;
        rep(i, 0, N) q[i + 1] = q[i] * (c - 1);
        mint tmp = p[deg[0]];
        rep(i, 1, (deg[0] - 1) / 2 + 1){
            tmp -= table.C(deg[0], i) * q[i] * c;
        }
        dp[c] = tmp;
        rep(i, 1, N){
            // cout << c << " : " << dp[c].val() << "\n";
            tmp = p[deg[i] - 1];
            rep(j, 1, (deg[i] - 1) / 2 + 1){
                tmp -= table.C(deg[i], j) * q[j];
            }
            dp[c] *= tmp;
        }
    }
    mint ans = 0;
    rep(i, 1, C + 1){
        // cout << i << " " << dp[i].val() << "\n";
        ans += dp[i] * table.C(C, i) * ((C - i) & 1 ? -1 : 1);
    }
    cout << ans.val() << "\n";
}