結果

問題 No.1044 正直者大学
ユーザー minato
提出日時 2020-05-01 22:50:58
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 2,000 ms
コード長 3,692 bytes
コンパイル時間 3,823 ms
コンパイル使用メモリ 200,444 KB
実行使用メモリ 6,400 KB
最終ジャッジ日時 2024-12-25 13:50:19
合計ジャッジ時間 4,226 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 28
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

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
using ll = long long;
using ull = unsigned long long; 
using pii =  pair<int, int>;
using pll =  pair<long long, long long>;
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define all(x) (x).begin(),(x).end()
constexpr char ln =  '\n';
constexpr long long MOD = 1000000007LL;
//constexpr long long MOD = 998244353LL;
template<class T, class U> inline bool chmax(T &a, U b) { if (a < b) { a = b; return true;} return false; }
template<class T, class U> inline bool chmin(T &a, U b) { if (a > b) { a = b; return true;} return false; }
////////////////////////////////////////////////////////////////////////////////////////////////////////////
template <std::uint_fast64_t Modulus> 
struct ModInt {
    using u64 = std::uint_fast64_t;
    u64 a;
    constexpr ModInt(const long long x = 0) noexcept : a(x >= 0 ? x % Modulus : (Modulus - (-x) % Modulus) % Modulus) {}
    constexpr u64 &value() noexcept { return a; }
    constexpr const u64 &value() const noexcept { return a; }
    constexpr ModInt operator+(const ModInt rhs) const noexcept {return ModInt(*this) += rhs;}
    constexpr ModInt operator-(const ModInt rhs) const noexcept {return ModInt(*this) -= rhs;}
    constexpr ModInt operator*(const ModInt rhs) const noexcept {return ModInt(*this) *= rhs;}
    constexpr ModInt operator/(const ModInt rhs) const noexcept {return ModInt(*this) /= rhs;}
    constexpr ModInt operator^(const long long rhs) const noexcept {return ModInt(*this) ^= rhs;}
    constexpr ModInt &operator+=(const ModInt rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt rhs) noexcept {
        if (a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr ModInt &operator/=(ModInt rhs) noexcept {
        u64 exp = Modulus - 2;
        while (exp) {
            if (exp&1) *this *= rhs;
            exp >>= 1;
            rhs *= rhs;
        }
        return *this;
    }
    constexpr ModInt &operator^=(long long exp) noexcept {
        ModInt rhs = a;
        a = 1;
        while (exp) {
            if (exp&1) *this *= rhs;
            exp >>= 1;
            rhs *= rhs;
        }
        return *this;
    }
    bool operator==(const ModInt &p) const {return a == p.a;}
    bool operator!=(const ModInt &p) const {return a != p.a;}
};
using mint = ModInt<MOD>;
struct ModCombination {
    vector<mint> Fac;
    vector<mint> Facinv;
    ModCombination(int x) {
        Fac.resize(x+1);
        Facinv.resize(x+1);
        Fac[0] = 1;
        for (int i = 0; i < x; ++i) Fac[i+1] = Fac[i]*(i+1);
        Facinv[x] = Fac[0]/Fac[x];
        for (int i = x; i > 0; --i) Facinv[i-1] = Facinv[i]*i;
    }
    mint get(int n, int k) {
        if (k < 0 || k > n) return 0;
        return Fac[n]*Facinv[k]*Facinv[n-k];
    }
};
int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int N,M,K; cin >> N >> M >> K;
    ModCombination MC(N+M);
    mint ans = 0;
    for (int i = K; i <= N+M; i++) {
        if (N-M+i >= 0 and (N-M+i)%2==0) {
            int num = (N-M+i)/2;
            if (N - num < 1 or M - (i - num) < 1 or i - num < 0) continue;
            int n = N - num;
            ans += MC.get(N-1,n-1)*MC.get(M-1,n-1)/n;
        }
    }
    ans *= MC.Fac[N]*MC.Fac[M];
    cout << ans.a << ln;
}
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