結果
| 問題 | No.3771 Leq-K Partition Multiplied |
| コンテスト | |
| ユーザー |
👑  potato167
|
| 提出日時 | 2026-10-17 04:26:43 |
| 言語 | C++17 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 1,574 ms / 8,000 ms |
| + 909µs | |
| コード長 | 14,361 bytes |
| 記録 | |
| コンパイル時間 | 3,637 ms |
| コンパイル使用メモリ | 275,260 KB |
| 実行使用メモリ | 207,940 KB |
| 最終ジャッジ日時 | 2026-10-17 04:27:03 |
| 合計ジャッジ時間 | 19,158 ms |
|
ジャッジサーバーID （参考情報） |
judge4_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 12 |
ソースコード
#line 1 "g.cpp"
#include <bits/stdc++.h>
#line 3 "g.cpp"
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_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 j = 0; j < len; j++) res[j + zero] = g[j] * c;
return res;
}
return res;
}
}
#line 3 "/Users/Shared/po167_library/fps/FPS_composition.hpp"
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 28 "g.cpp"
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 30 "g.cpp"
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(){
po167::Binomial<mint> table;
int N, K;
ll M, X;
cin >> N >> M >> K >> X;
vector<mint> e(N + 1);
rep(i, 1, N + 1) e[i] = table.invfact(i);
auto f = po167::FPS_pow(e, K);
mint tmp = 1;
rep(i, 0, K) tmp *= M - 1 - i;
rep(i, 0, N + 1) f[i] *= tmp * table.invfact(K) * table.fact(i);
vector<mint> ans(N + 1);
vector<mint> base(N + 1);
rep(i, 0, N + 1) base[i] = (mint(M)).pow(i);
/*rep(i, 0, N + 1) {
rep(k, 0, N) ans[k + 1] += base[k] * ((mint(i + 1)).pow(X) - (mint(i)).pow(X));
base = atcoder::convolution(base, f);
}*/
vector<mint> pw(N + 1);
rep(i, 0, N + 1) {
pw[i] = (mint(i + 1)).pow(X) - (mint(i)).pow(X);
}
ans = po167::FPS_comp(pw, f);
ans = atcoder::convolution(base, ans);
ans = atcoder::convolution(ans, {0, 1});
rep(i, 1, N + 1) {
ans[i] *= M;
cout << ans[i].val() << "\n";
}
}
/*
* 最初の値は無視する
* すると、
* x^{K - 1} / (1 - x) * (M - 1) * (1 / (1 - 2x)) * (M - 2) ... * (M - K) で
* ダメになる
* z 回必要とは
* 上の多項式を f(x) として、
* f(x)^z の n未満 次数
* つまり
* [x^{n - 1}] f(x)^z * (1 / (1 - Mx))
* X乗しないといけないんだった
* X = 1 なら
* base * (1 + f + f^2 + ... ) で良い
* X 乗の時、
* base * (1 + sum f^{i}((i + 1)^{X} - i^{X}))
* comp をすればいいのか
*/