#474916 (C++11) No.1044 正直者大学

• 問題: No.1044 正直者大学
• ユーザー: packer_jp
• 提出日時: 2020-05-01 23:09:24
• 言語: C++11 (gcc 11.4.0)
• 結果: AC
• 実行時間: 24 ms / 2,000 ms
• コード長: 5,542 bytes
• コンパイル時間: 1,723 ms
• コンパイル使用メモリ: 164,608 KB
• 実行使用メモリ: 8,028 KB
• 最終ジャッジ日時: 2024-06-07 11:25:12
• 合計ジャッジ時間: 2,969 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	16 ms; 8,028 KB
testcase_06	AC	24 ms; 8,028 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	8 ms; 5,704 KB
testcase_13	AC	14 ms; 6,360 KB
testcase_14	AC	9 ms; 6,104 KB
testcase_15	AC	16 ms; 7,644 KB
testcase_16	AC	17 ms; 7,512 KB
testcase_17	AC	9 ms; 5,464 KB
testcase_18	AC	11 ms; 5,472 KB
testcase_19	AC	6 ms; 5,376 KB
testcase_20	AC	4 ms; 5,376 KB
testcase_21	AC	5 ms; 5,376 KB
testcase_22	AC	7 ms; 5,468 KB
testcase_23	AC	13 ms; 7,516 KB
testcase_24	AC	9 ms; 5,976 KB
testcase_25	AC	8 ms; 5,596 KB
testcase_26	AC	13 ms; 7,516 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	1 ms; 5,376 KB
testcase_29	AC	1 ms; 5,376 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define rep(i, n) for (int i = 0; i < (n); i++)
#define reps(i, n) for (int i = 1; i <= (n); i++)
#define all(x) begin(x), end(x)
#define uniq(x) (x).erase(unique(all(x)), end(x))
#define bit(n) (1LL << (n))
#define cdiv(a, b) (((a) - 1) / (b) + 1)
#define dump(x) cerr << #x " = " << (x) << endl
using vint = vector<int>;
using vvint = vector<vint>;
using pint = pair<int, int>;
using vpint = vector<pint>;
template<typename T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
constexpr long double PI = 3.1415926535897932384626433832795028L;
constexpr int DY[8] = {0, 1, 0, -1, 1, 1, -1, -1};
constexpr int DX[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int gcd(int a, int b) {
    while (b) { swap(a %= b, b); }
    return a;
}
int lcm(int a, int b) { return a / gcd(a, b) * b; }
template<typename T> void fin(T mes) {
    cout << mes << endl;
    exit(0);
}
template<typename T, typename U> bool chmax(T &a, const U &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template<typename T, typename U> bool chmin(T &a, const U &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}
template<typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &rhs) {
    os << "(" << rhs.first << ", " << rhs.second << ")";
    return os;
}
template<typename T> ostream &operator<<(ostream &os, const vector<T> &rhs) {
    os << "{";
    for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
        os << *itr << (next(itr) != rhs.end() ? ", " : "");
    }
    os << "}";
    return os;
}
struct setup {
    static constexpr int PREC = 20;
    setup() {
        cout << fixed << setprecision(PREC);
        cerr << fixed << setprecision(PREC);
    };
} setup;

template<int MOD = 1000000007>
struct mod_int {
    int val;
    mod_int(long long val_ = 0) : val(val_ % MOD) { if (val < 0) { val += MOD; }}
    bool operator==(const mod_int &rhs) const { return val == rhs.val; }
    bool operator!=(const mod_int &rhs) const { return std::rel_ops::operator!=(*this, rhs); }
    mod_int &operator+=(const mod_int &rhs) {
        if ((val += rhs.val) >= MOD) { val -= MOD; }
        return *this;
    }
    mod_int &operator-=(const mod_int &rhs) {
        if ((val += MOD - rhs.val) >= MOD) { val -= MOD; }
        return *this;
    }
    mod_int &operator*=(const mod_int &rhs) {
        val = (int) ((long long) val * rhs.val % MOD);
        return *this;
    }
    mod_int &operator/=(const mod_int &rhs) { return *this *= rhs.inv(); }
    mod_int operator+() const { return *this; }
    mod_int operator-() const { return -val; }
    mod_int operator++() { return *this += 1; }
    mod_int operator--() { return *this -= 1; }
    mod_int operator++(signed) {
        const mod_int ret(*this);
        ++*this;
        return ret;
    }
    mod_int operator--(signed) {
        const mod_int ret(*this);
        --*this;
        return ret;
    }
    mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }
    mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }
    mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }
    mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }
    mod_int inv() const {
        int a = val, b = MOD, x = 1, u = 0;
        while (b) {
            int t = a / b;
            std::swap(a -= t * b, b);
            std::swap(x -= t * u, u);
        }
        return x;
    }
    mod_int pow(long long n) const {
        if (n < 0) { return pow(-n).inv(); }
        mod_int ret = 1, mul = *this;
        while (n) {
            if (n & 1) { ret *= mul; }
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend std::istream &operator>>(std::istream &is, mod_int &rhs) {
        long long v;
        is >> v;
        rhs = v;
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const mod_int &rhs) { return os << rhs.val; }
    struct combination {
        std::vector<mod_int> fact{1, 1}, f_inv{1, 1}, inv{0, 1};
        void calc(int n) {
            while (fact.size() <= n) {
                int i = fact.size();
                fact.push_back(fact[i - 1] * i);
                inv.push_back(-inv[MOD % i] * (MOD / i));
                f_inv.push_back(f_inv[i - 1] * inv[i]);
            }
        }
        mod_int P(int n, int r) { return r < 0 || n < r ? 0 : (calc(n), fact[n] * f_inv[n - r]); }
        mod_int C(int n, int r) { return r < 0 || n < r ? 0 : (calc(n), fact[n] * f_inv[r] * f_inv[n - r]); }
        mod_int H(int n, int r) { return C(n + r - 1, r); }
    };
};

using mint = mod_int<>;
mint::combination comb;
int N, M, K;
signed main() {
    cin >> N >> M >> K;
    comb.calc(N + M);
    if (N == 1) {
        if (N + M - 2 >= K) { fin(comb.fact[M]); }
        else { fin(0); }
    }
    if (M == 1) {
        if (N + M - 2 >= K) { fin(comb.fact[N]); }
        else { fin(0); }
    }
    mint ans = 0;
    reps(i, min(N, M)) {
        if (K > N + M - 2 * i) { break; }
        ans += comb.fact[N - 1] * comb.fact[M] * comb.C(N - 2, i - 2) * comb.C(M - 1, i - 1);
        ans += comb.fact[N - 1] * comb.fact[M] * comb.C(N - 2, i - 1) * comb.C(M - 1, i - 1);
        ans += comb.fact[N - 1] * comb.fact[M] * comb.C(N - 2, i - 1) * comb.C(M - 1, i - 1);
        ans += comb.fact[N - 1] * comb.fact[M] * comb.C(N - 2, i - 0) * comb.C(M - 1, i - 1);
    }
    cout << ans << endl;
}