結果
問題 | No.2514 Twelvefold Way Returns |
ユーザー |
👑 ![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 38 |
ソースコード
#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;}