#1176086 (C++17) No.3619 Compositional Power with Schröder Coordinate

• 問題: No.3619 Compositional Power with Schröder Coordinate
• ユーザー: 👑 potato167
• 提出日時: 2026-08-10 21:49:40
• 言語: C++17 (gcc 15.2.0 + boost 1.90.0)
• 結果: AC
• 実行時間: 1,047 ms / 10,000 ms
• コード長: 4,934 bytes
• コンパイル時間: 2,531 ms
• コンパイル使用メモリ: 258,724 KB
• 実行使用メモリ: 202,556 KB
• 最終ジャッジ日時: 2026-08-10 21:49:51
• 合計ジャッジ時間: 10,417 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge2_0

ファイルパターン	結果
sample	AC * 2
other	AC * 6

ソースコード

#line 1 "a.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+=(int)(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}

#line 2 "/Users/Shared/po167_library/fps/FPS_composition.hpp"
#include <atcoder/convolution>

namespace po167{
// n = |g|
// return f(g(x))
// https://maspypy.com/fps-合成・逆関数の解説（2）転置原理による合成ア
template<class T>
std::vector<T> FPS_comp(std::vector<T> f, std::vector<T> g){
    assert(g[0] == 0);
    auto rec = [&](auto rec, int n, int k, std::vector<T> Q) -> std::vector<T> {
        if (n == 1){
            std::vector<T> p(2 * k);
            std::reverse(f.begin(), f.end());
            for (int i = 0; i < k; i++) p[2 * i] = f[i];
            return p;
        }
        std::vector<T> nxt_Q(2 * n * k);
        for (int i = 0; i < n * k; i++) nxt_Q[n * k + i] += Q[i * 2] * 2;
        Q.resize(4 * n * k);
        atcoder::internal::butterfly(Q);
        // Q(-x)
        std::vector<T> R(4 * n * k);
        for (int i = 0; i < 2 * n * k; i++){
            R[i * 2] = Q[i * 2 + 1];
            R[i * 2 + 1] = Q[i * 2];
        }
        T iz = (T)(1) / (T)(4 * n * k);
        for (int i = 0; i < 4 * n * k; i++) Q[i] *= R[i];
        for (int i = 0; i < 2 * n * k; i++) Q[i] = Q[i * 2];
        Q.resize(2 * n * k);
        atcoder::internal::butterfly_inv(Q);
        for (int i = 0; i < 2 * n * k; i++) nxt_Q[i] += Q[i] * iz * 2;
        for (int j = 0; j < 2 * k; j++) for (int i = n / 2; i < n; i++){
            nxt_Q[n * j + i] = 0;
        }
        std::vector<T> pq = rec(rec, n / 2, k * 2, nxt_Q);
        std::vector<T> p(2 * n * k);
        for (int j = 0; j < 2 * k; j++) for (int i = n / 2; i < n; i++){
            pq[n * j + i] = 0;
        }
        for (int i = 0; i < n * k; i++) p[i * 2 + 1] += pq[n * k + i];
        std::reverse(pq.begin(), pq.end());
        atcoder::internal::butterfly(pq);
        pq.resize(4 * n * k);
        for (int i = 2 * n * k - 1; i >= 0; i--){
            pq[i * 2 + 1] = pq[i];
            pq[i * 2] = pq[i];
        }
        for (int i = 0; i < 4 * n * k; i++) pq[i] *= R[i];
        atcoder::internal::butterfly_inv(pq);
        for (int i = 0; i < 2 * n * k; i++) p[i] += pq[4 * n * k - 1 - i] * iz;
        return p;
    };
    int N = (int)g.size();
    int n = 1;
    while (n < N) n *= 2;
    f.resize(n, 0);
    g.resize(n, 0);
    std::vector<T> Q(2 * n);
    for (int i = 0; i < n; i++) Q[i] = -g[i];
    auto p = rec(rec, n, 1, Q);
    std::vector<T> res(n);
    for (int i = 0; i < n; i++) res[i] = p[i];
    std::reverse(res.begin(), res.end());
    res.resize(N);
    return res;
}
}
#line 26 "a.cpp"
using mint = atcoder::modint998244353;

void solve();
// DEAR MYSTERIES / 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, M;
    cin >> N >> M;
    vector<mint> f(N), g(N), h(N);
    rep(i, 0, N) {
        int a;
        cin >> a;
        f[i] = a;
    }
    rep(i, 0, N) {
        int a;
        cin >> a;
        g[i] = a;
    }
    rep(i, 0, N) {
        int a;
        cin >> a;
        h[i] = a;
    }
    mint tmp = f[1].pow(M);
    for (auto &x : g) x *= tmp;
    auto ans = po167::FPS_comp(h, g);
    rep(i, 0, N) {
        cout << ans[i].val() << (i + 1 == N ? '\n' : ' ');
    }
}

/*
 *
 * f^m(x) = h(g(f^m(x)))
 * = h(a1 * g(f^{m - 1}(x))
 *
 */