結果

問題 No.2876 Infection
ユーザー 👑 potato167
提出日時 2024-09-06 22:22:05
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 6,237 bytes
コンパイル時間 3,481 ms
コンパイル使用メモリ 238,096 KB
最終ジャッジ日時 2025-02-24 04:32:55
ジャッジサーバーID
(参考情報)
judge1 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 24 RE * 3
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ソースコード

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プレゼンテーションモードにする

#line 1 "a.cpp"
#include <bits/stdc++.h>
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
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> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll 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(a>b){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=0){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+=(a&1),a>>=1;}return res;}
template<class T> bool inside(T l,T x,T r){return l<=x&&x<r;}
#include <atcoder/modint>
using mint = atcoder::modint998244353;
#line 2 "/Users/Shared/po167_library/fps/Taylor_Shift.hpp"
#include <atcoder/convolution>
#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);
}
};
}
#line 5 "/Users/Shared/po167_library/fps/Taylor_Shift.hpp"
namespace po167{
// return f(x + c)
template<class T>
std::vector<T> Taylor_Shift(
std::vector<T> f, T c
){
int n = f.size();
Binomial<T> table(n);
std::vector<T> g(n);
T tmp = 1;
for (int i = 0; i < n; i++){
g[n - 1 - i] = table.invfact(i) * tmp;
tmp *= c;
f[i] *= table.fact(i);
}
// using cyclic convolution is faster ?
g = atcoder::convolution(f, g);
std::vector<T> res(n);
for (int i = 0; i < n; i++){
res[i] = table.invfact(i) * g[n + i - 1];
}
return res;
}
}
#line 32 "a.cpp"
void solve();
// CYAN / FREDERIC
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1;
// cin >> t;
rep(i, 0, t) solve();
}
void solve(){
int N, x;
cin >> N >> x;
mint p = (mint)(x) / (mint)(100);
mint q = 1 - p;
if (x == 0){
cout << 1 << "\n";
return;
}
if (x == 100){
cout << N << "\n";
}
vector<mint> dp(N);
mint ans = 0;
dp[N - 1] = 1;
for (int i = N - 1; i >= 0; i--){
mint tmp = 1;
for (auto &y : dp) y *= tmp, tmp *= q;
dp = po167::Taylor_Shift(dp, p / q);
ans += (mint)(N - i) * dp.back();
dp.pop_back();
}
cout << ans.val() << "\n";
}
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