test/fps/sum_of_power.test.cpp

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Last update: 2025-03-19 04:02:58+09:00
Problem: https://yukicoder.me/problems/no/1145

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Code

#define PROBLEM "https://yukicoder.me/problems/no/1145"
#include "../../fps/FPS_sum_of_power.hpp"
#include <iostream>

int main(){
	std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int N, M;
    std::cin >> N >> M;
    std::vector<atcoder::modint998244353> A(N);
    for (int i = 0; i < N; i++){
        int a;
        std::cin >> a;
        A[i] = a;
    }
    auto ans = po167::FPS_sum_of_power(A, M);
    for (int i = 1; i <= M; i++){
        std::cout << ans[i].val() << (i == M ? "\n" : " ");
    }
}

#line 1 "test/fps/sum_of_power.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1145"
#line 2 "fps/FPS_log.hpp"
#include <vector>
#line 3 "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 "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 "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 "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 "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 "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 3 "test/fps/sum_of_power.test.cpp"
#include <iostream>

int main(){
	std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int N, M;
    std::cin >> N >> M;
    std::vector<atcoder::modint998244353> A(N);
    for (int i = 0; i < N; i++){
        int a;
        std::cin >> a;
        A[i] = a;
    }
    auto ans = po167::FPS_sum_of_power(A, M);
    for (int i = 1; i <= M; i++){
        std::cout << ans[i].val() << (i == M ? "\n" : " ");
    }
}