結果
| 問題 | No.3515 Anti EIKO |
| コンテスト | |
| ユーザー |
👑  potato167
|
| 提出日時 | 2026-04-24 21:45:06 |
| 言語 | C++17 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 6,617 bytes |
| 記録 | |
| コンパイル時間 | 2,868 ms |
| コンパイル使用メモリ | 261,216 KB |
| 実行使用メモリ | 6,400 KB |
| 最終ジャッジ日時 | 2026-04-24 21:45:19 |
| 合計ジャッジ時間 | 4,783 ms |
|
ジャッジサーバーID （参考情報） |
judge2_1 / judge3_1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 31 |
ソースコード
#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+=(int)(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}
#line 3 "/Users/Shared/po167_library/fps/FPS_Boston_Mori.hpp"
#include <atcoder/convolution>
#line 4 "/Users/Shared/po167_library/fps/FPS_extend.hpp"
namespace po167{
// in : DFT(v) (len(v) = z)
// out : DFT(v) (len(v) = 2 * z)
template<class T>
void FPS_extend(std::vector<T> &v){
int z = v.size();
T e = (T(atcoder::internal::primitive_root_constexpr(T::mod()))).pow(T::mod() / (2 * z));
auto cp = v;
atcoder::internal::butterfly_inv(cp);
T tmp = (T)(1) / (T)(z);
for (int i = 0; i < z; i++){
cp[i] *= tmp;
tmp *= e;
}
atcoder::internal::butterfly(cp);
for (int i = 0; i < z; i++) v.push_back(cp[i]);
};
}
#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 7 "/Users/Shared/po167_library/fps/FPS_Boston_Mori.hpp"
namespace po167{
// return [x^k] P(x) / Q(x)
template<class T>
T Boston_Mori(long long k, std::vector<T> P, std::vector<T> Q){
assert(!Q.empty() && Q[0] != 0);
// fast
if ((int)Q.size() > 60){
int z = 1;
while (z < (int)std::max(P.size(), Q.size())) z *= 2;
P.resize(z * 2, 0);
Q.resize(z * 2, 0);
atcoder::internal::butterfly(P);
atcoder::internal::butterfly(Q);
while (k){
// Q(-x)
std::vector<T> Q_n(z * 2);
for (int i = 0; i < z; i++){
Q_n[i * 2] = Q[i * 2 + 1];
Q_n[i * 2 + 1] = Q[i * 2];
}
for (int i = 0; i < z * 2; i++){
P[i] *= Q_n[i];
Q[i] *= Q_n[i];
}
FPS_pick_even_odd(P, k & 1);
FPS_pick_even_odd(Q, 0);
k /= 2;
if (k == 0) break;
FPS_extend(P);
FPS_extend(Q);
}
T SP = 0, SQ = 0;
for (int i = 0; i < z; i++) SP += P[i], SQ += Q[i];
return SP / SQ;
}
// simple
while (k){
auto n_Q = Q;
for (int i = 0; i < int(Q.size()); i++){
if (i & 1) n_Q[i] *= -1;
}
auto n_P = atcoder::convolution(P, n_Q);
n_Q = atcoder::convolution(Q, n_Q);
for (int i = 0; i < int(Q.size()); i++){
Q[i] = n_Q[i * 2];
}
P.clear();
for (int i = (k & 1); i < int(n_P.size()); i += 2){
P.push_back(n_P[i]);
}
k >>= 1;
}
return P[0] / Q[0];
}
template<class T>
// 0 = a[i] * c[0] + a[i - 1] * c[1] + a[i - 2] * c[2] + ... + a[i - d] * c[d]
// a.size() + 1 == c.size()
// c[0] = - 1 ?
// return a[k]
T Kth_Linear(long long k, std::vector<T> a, std::vector<T> c){
int d = a.size();
assert(d + 1 == int(c.size()));
std::vector<T> P = atcoder::convolution(a, c);
P.resize(d);
return Boston_Mori(k, P, c);
}
};
#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 27 "e.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(){
ll N, K;
cin >> N >> K;
vector<mint> f0(4 * N + 1), f1 = {1, -1};
mint inv = (mint(5)).inv();
f0.back() = inv.pow(N * 4);
vector<mint> g0(N * 4 + 1);
rep(i, 0, N) {
g0[i * 4] = inv.pow(i * 4);
}
auto g1 = f1;
g0 = atcoder::convolution(g0, g1);
po167::FPS_add(g0, f0);
auto ans = po167::Boston_Mori(K, f0, g0);
cout << ans.val() << "\n";
}
/*
* 最初から栄光になるまで
* f(x) = (x / 5)^{4N} / (1 - x)
* 栄光から栄光になるまで
* g(x) = f(x) + (1 - (x / 5)^{4N}) / (1 - (x / 5)^{4})
*
* h(x) * g(x) = f(x)
* h(x) = f(x) / g(x)
*
* もっといい計算量で解けるじゃん
* 栄光の勝ちという事で
*
*/