結果

問題 No.1044 正直者大学
コンテスト
ユーザー kcvlex
提出日時 2020-05-01 22:21:42
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 59 ms / 2,000 ms
コード長 5,880 bytes
コンパイル時間 2,267 ms
コンパイル使用メモリ 152,820 KB
最終ジャッジ日時 2025-01-10 05:06:22
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 # 

#include <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#include <variant>
#define endl codeforces
#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)
using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;
template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }
template <typename T> T make_v(T init) { return init; }
template <typename T, typename... Tail> auto make_v(T init, std::size_t s, Tail... tail) { auto v = std::move(make_v(init, tail...)); return vec<decltype(v)>(s, v); }
template <typename T, std::size_t Head, std::size_t... Tail> struct multi_dem_array { using type = std::array<typename multi_dem_array<T, Tail...>::type, Head>; };
template <typename T, std::size_t Head> struct multi_dem_array<T, Head> { using type = std::array<T, Head>; };
template <typename T, std::size_t... Args> using mdarray = typename multi_dem_array<T, Args...>::type;
namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; }

namespace math {

template <typename T>
constexpr T pow(const T &n, ll k) {
    T ret = n.mul_id_ele();
    T cur = n;
    while (k) {
        if (k & 1) ret *= cur;
        cur *= cur;
        k /= 2;
    }
    return ret;
}

}

namespace math {

template <ll Mod>
struct Modint {

    constexpr Modint(ll x) noexcept : x((Mod + x % Mod) % Mod) { }
    
    constexpr Modint() noexcept : Modint(0) { }
    
    constexpr Modint<Mod> add_id_ele() const noexcept { 
        return Modint<Mod>(0); 
    }
    
    constexpr Modint<Mod> mul_id_ele() const noexcept {
        return Modint<Mod>(1); 
    }
    
    constexpr ll& value() noexcept { 
        return x; 
    }
    
    constexpr ll value() const noexcept {
        return x; 
    }

    constexpr Modint& operator +=(const Modint &oth) noexcept {
        x += oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator -=(const Modint &oth) noexcept {
        x += Mod - oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator *=(const Modint &oth) noexcept {
        x *= oth.value();
        x %= Mod;
        return *this;
    }

    constexpr Modint& operator /=(const Modint &oth) noexcept {
        x *= oth.inv();
        x %= Mod;
        return *this;
    }

    constexpr Modint operator +(const Modint &oth) const noexcept {
        return Modint(x) += oth;
    }

    constexpr Modint operator -(const Modint &oth) const noexcept {
        return Modint(x) -= oth;
    }

    constexpr Modint operator *(const Modint &oth) const noexcept {
        return Modint(x) *= oth;
    }

    constexpr Modint operator /(const Modint &oth) const noexcept {
        return Modint(x) /= oth;
    }

    constexpr Modint operator -() const noexcept {
        return Modint((x != 0) * (Mod - x)); 
    }

    template <typename T>
    constexpr typename std::enable_if<std::is_integral<T>::value, const Modint&>::type
    operator =(T t) noexcept {
        (*this) = Modint(std::forward<T>(t)); 
        return *this;
    }

    constexpr Modint inv() const noexcept {
        return ::math::pow(*this, Mod - 2);
    }

    constexpr ll mod() const noexcept {
        return Mod;
    }

private:
    ll x;
};

}

namespace math {

template <ll Mod>
class Factorial {
    using mint = Modint<Mod>;

    ssize_t maxv;
    vec<mint> factv, ifactv;

public:
    Factorial(ssize_t maxv) : maxv(maxv), factv(maxv + 1), ifactv(maxv + 1) {
        factv[0] = mint(1);
        for (ll i = 1; i <= maxv; i++) factv[i] = factv[i - 1] * i;
        ifactv.back() = factv.back().inv();
        for (ll i = maxv - 1; 0 <= i; i--) ifactv[i] = ifactv[i + 1] * (i + 1);
    }

    mint fact(ll n) const {
        return factv[n]; 
    }

    mint ifact(ll n) const {
        return ifactv[n];
    }

    mint perm(ll n, ll k) const {
        return factv[n] * ifactv[n - k];
    }

    mint comb(ll n, ll k) const {
        return perm(n, k) * ifactv[k];
    }
};

}

const ll mod = 1e9 + 7;
using mint = math::Modint<mod>;
math::Factorial<mod> fa(1e6);

int main() {
    ll n, m, k;
    std::cin >> n >> m >> k;
    mint ans = 0;
    for (ll i = 2; i / 2 <= std::min(n, m); i += 2) {
        ll cnt = n + m - i;
        if (cnt < k) break;
        mint p = 1;
        for (ll e : { n, m, }) {
            p *= fa.comb(e - 1, i / 2 - 1);
            p *= fa.fact(e);
        }
        p *= mint(i / 2).inv();
        ans += p;
    }
    std::cout << ans.value() << "\n";
    return 0;
}
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