#1176089 (C++17) No.3620 Compositional Power with Schröder Coordinate 2

• 問題: No.3620 Compositional Power with Schröder Coordinate 2
• ユーザー: 👑 potato167
• 提出日時: 2026-08-10 22:03:07
• 言語: C++17 (gcc 15.2.0 + boost 1.90.0)
• 結果: AC
• 実行時間: 1,470 ms / 10,000 ms
• コード長: 10,743 bytes
• コンパイル時間: 2,629 ms
• コンパイル使用メモリ: 265,628 KB
• 実行使用メモリ: 24,776 KB
• 最終ジャッジ日時: 2026-08-11 00:00:25
• 合計ジャッジ時間: 12,027 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge3_0

ファイルパターン	結果
sample	AC * 2
other	AC * 7

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 4 "/Users/Shared/po167_library/fps/FPS_Power_Projection.hpp"

#line 3 "/Users/Shared/po167_library/fps/FPS_pick_even_odd.hpp"

namespace po167{
// s.t |v| = 2 ^ s (no assert)
template<class T>
void FPS_pick_even_odd(std::vector<T> &v, int odd){
    int z = v.size() / 2;
    T half = (T)(1) / (T)(2);
    if (odd == 0){
        for (int i = 0; i < z; i++){
            v[i] = (v[i * 2] + v[i * 2 + 1]) * half;
        }
        v.resize(z);
    } else {
        T e = (T(atcoder::internal::primitive_root_constexpr(T::mod()))).pow(T::mod() / (2 * z));
        T ie = T(1) / e;
        std::vector<T> es = {half};
        while ((int)es.size() != z){
            std::vector<T> n_es((int)es.size() * 2);
            for (int i = 0; i < (int)es.size(); i++){
                n_es[i * 2] = (es[i]);
                n_es[i * 2 + 1] = (es[i] * ie);
            }
            ie *= ie;
            std::swap(n_es, es);
        }
        for (int i = 0; i < z; i ++){
            v[i] = (v[i * 2] - v[i * 2 + 1]) * es[i];
        }
        v.resize(z);
    }
}
}
#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 7 "/Users/Shared/po167_library/fps/FPS_Power_Projection.hpp"

namespace po167{
// n = |g|
// return 
// for i = 0, 1, ... , m - 1
//     [x ^ {n - 1}] g(x) f(x) ^ i
template<class T>
std::vector<T> Power_Projection(std::vector<T> g, std::vector<T> f, int m){
    assert(f[0] == 0);
    int ind = (int)g.size() - 1;
    int n = 1;
    while(n < (int)g.size()) n *= 2;
    f.reserve(4 * n);
    g.reserve(4 * n);
    g.resize(n, 0);
    f.resize(n, 0);
    std::vector<T> hold_f(n), hold_g(n);
    // g(x) / (y - f(x))
    for (auto &x : f) x *= -1;
    int nk = n;
    T iz = (T)(1) / (T)(2 * n);
    while (nk != 1){
        hold_g = g;
        hold_f = f;
        // n -> 4 * n
        g.resize(4 * n);
        f.resize(4 * n);
        for (int i = n / nk - 1; i >= 0; i--){
            for (int j = nk - 1; j >= 0; j--){
                g[i * nk * 2 + j] = g[i * nk + j];
                if (i) g[i * nk + j] = 0;
                f[i * nk * 2 + j] = f[i * nk + j];
                if (i) f[i * nk + j] = 0;
            }
        }
        // tran
        atcoder::internal::butterfly(g);
        atcoder::internal::butterfly(f);
        for (int i = 0; i < 2 * n; i++){
            g[i * 2] *= f[i * 2 + 1];
            g[i * 2 + 1] *= f[i * 2];
            f[i * 2] *= f[i * 2 + 1];
            f[i * 2 + 1] = f[i * 2];
        }
        FPS_pick_even_odd(g, (ind & 1));
        FPS_pick_even_odd(f, 0);
        atcoder::internal::butterfly_inv(g);
        atcoder::internal::butterfly_inv(f);
        for (auto &x : g) x *= iz;
        for (auto &x : f) x *= iz;
        // y ^ nk
        for (int i = 0; i < n; i++){
            if ((ind + i + 1) & 1)
                g[n + (i / nk) * nk + (i & (nk - 1)) / 2] += hold_g[i];
            if ((i & 1) == 0)
                f[n + (i / nk) * nk + (i & (nk - 1)) / 2] += hold_f[i] * 2;
        }
        nk /= 2;
        for (int i = 0; i < n; i++){
            g[i] = g[(i / nk) * nk * 2 + (i & (nk - 1))];
            f[i] = f[(i / nk) * nk * 2 + (i & (nk - 1))];
        }
        g.resize(n);
        f.resize(n);
        ind /= 2;
    }
    f.push_back(1);
    std::reverse(g.begin(), g.end());
    std::reverse(f.begin(), f.end());
    g.resize(m);
    std::vector<T> ans = atcoder::convolution(g, FPS_inv(f, m));
    ans.resize(m);
    return ans;
}
}
#line 3 "/Users/Shared/po167_library/fps/FPS_add.hpp"

namespace po167{
template <class T>
// a(x) += b(x) * c * x^d
void FPS_add(std::vector<T> &a, std::vector<T> b, T c = 1, int d = 0){
    for (int i = 0; i < (int)(b.size()); i++){
        while ((int)a.size() <= i + d) a.push_back((T)0);
        a[i + d] += b[i] * c;
    }
}
}
#line 28 "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;
    }
    vector<mint> init(N);
    init[0] = 1;
    auto tmp = po167::Power_Projection(init, g, N);
    vector<mint> ans(M);
    rep(i, 0, N) tmp[i] *= h[i];

    /*{
        rep(i, 0, M) rep(j, 0, N) {
            ans[i] += f[1].pow(i * j) * tmp[j];
        }
    }*/
    auto calc = [&](auto self, int l, int r) -> pair<vector<mint>, vector<mint>> {
        if (l + 1 == r) {
            return {{tmp[l]}, {1, -f[1].pow(l)}};
        }
        int m = (l + r) / 2;
        auto [Lc, Lp] = self(self, l, m);
        auto [Rc, Rp] = self(self, m, r);
        auto C = atcoder::convolution(Lc, Rp);
        po167::FPS_add(C, atcoder::convolution(Lp, Rc));
        return {C, atcoder::convolution(Lp, Rp)};
    };
    auto [A, B] = calc(calc, 0, N);
    ans = atcoder::convolution(po167::FPS_inv(B, M), A);
    rep(i, 0, M) {
        cout << ans[i].val() << (i + 1 == M ? "\n" : " ");
    }
}

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