結果

問題 No.2514 Twelvefold Way Returns
ユーザー 👑 Nachia
提出日時 2023-10-20 23:34:03
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 61 ms / 3,000 ms
コード長 3,283 bytes
コンパイル時間 930 ms
コンパイル使用メモリ 83,392 KB
最終ジャッジ日時 2025-02-17 11:11:25
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 38
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#line 1 "..\\Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <atcoder/modint>
#line 3 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\combination.hpp"
namespace nachia{
template<class Modint>
class Comb{
private:
static constexpr int MOD = Modint::mod();
std::vector<Modint> F;
std::vector<Modint> iF;
public:
void extend(int newN){
int prevN = (int)F.size() - 1;
if(newN >= MOD) newN = MOD - 1;
if(prevN >= newN) return;
F.resize(newN+1);
iF.resize(newN+1);
for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
iF[newN] = F[newN].inv();
for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
}
Comb(int n = 1){
F.assign(2, Modint(1));
iF.assign(2, Modint(1));
extend(n);
}
Modint factorial(int n) const { return F[n]; }
Modint invFactorial(int n) const { return iF[n]; }
Modint invOf(int n) const { return iF[n] * F[n-1]; }
Modint comb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[r] * iF[n-r];
}
Modint invComb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[r] * F[n-r];
}
Modint perm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[n-r];
}
Modint invPerm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[n-r];
}
Modint operator()(int n, int r) const { return comb(n,r); }
};
} // namespace nachia
#line 7 "..\\Main.cpp"
using Modint = atcoder::static_modint<998244353>;
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;
struct F{
Modint a,b,c;
};
F operator+(F l, F r){ return { l.a+r.a, l.b+r.b, l.c+r.c }; }
F operator*(F l, F r){ return { l.a*r.a + l.b*r.c + l.c*r.b, l.a*r.b + l.b*r.a + l.c*r.c, l.a*r.c + l.b*r.b + l.c*r.a }; }
F Omega(i64 t){
t %= 3; t += 3; t %= 3;
if(t == 0) return { 1, 0, 0 };
if(t == 1) return { 0, 1, 0 };
return { 0, 0, 1 };
}
F powMod(F a, i64 i){
if(i == 0) return {1,0,0};
F f = powMod(a*a, i/2);
if(i%2 == 1) f = f * a;
return f;
}
ostream& operator<<(ostream& ostr, F f){ return ostr << "(" << f.a.val() << ' ' << f.b.val() << ' ' << f.c.val() << ")"; }
void testcase(){
auto comb = nachia::Comb<Modint>(1000);
i64 N, M; cin >> N >> M;
F Q = {0,0,0};
for(i64 a=0; a<=M; a++) for(i64 b=0; a+b<=M; b++){
i64 c = M - a - b;
F ex = { a, b, c };
//cout << "ex = " << ex << endl;
ex = powMod(ex, N);
//cout << "pow ex = " << ex << endl;
F t = F{ comb.factorial(M) / comb.factorial(a) / comb.factorial(b) / comb.factorial(c), 0, 0 };
Q = Q + ex * t * Omega(b+b+c);
}
//cout << Q.a.val() << " " << Q.b.val() << " " << Q.c.val() << endl;
Modint ans = (Q.a - (Q.b + Q.c) / 2) / Modint(3).pow(M);
cout << ans.val() << endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
//int T; cin >> T; rep(t,T)
testcase();
return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0