結果

問題 No.895 MESE
ユーザー kimiyuki
提出日時 2019-09-27 22:14:35
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 4,953 bytes
コンパイル時間 2,218 ms
コンパイル使用メモリ 199,868 KB
最終ジャッジ日時 2025-01-07 19:26:06
ジャッジサーバーID
（参考情報） 		judge2 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 26
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

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#define dump(x) cerr << #x " = " << x << endl
using namespace std;
template <class T> using reversed_priority_queue = priority_queue<T, vector<T>, greater<T> >;
template <class T, class U> inline void chmax(T & a, U const & b) { a = max<T>(a, b); }
template <class T, class U> inline void chmin(T & a, U const & b) { a = min<T>(a, b); }
template <typename X, typename T> auto make_table(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return 
    vector<decltype(cont)>(x, cont); }
template <typename T> ostream & operator << (ostream & out, vector<T> const & xs) { REP (i, (int)xs.size() - 1) out << xs[i] << ' '; if (not xs.empty
    ()) out << xs.back(); return out; }
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    inline mint<MOD> operator + (mint<MOD> other) const { int32_t c = this->value + other.value; return mint<MOD>(c >= MOD ? c - MOD : c); }
    inline mint<MOD> operator - (mint<MOD> other) const { int32_t c = this->value - other.value; return mint<MOD>(c <    0 ? c + MOD : c); }
    inline mint<MOD> operator * (mint<MOD> other) const { int32_t c = (int64_t)this->value * other.value % MOD; return mint<MOD>(c < 0 ? c + MOD : c
        ); }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (int64_t)this->value * other.value % MOD; if (this->value < 0) this->value += 
        MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0); }
    mint<MOD> pow(uint64_t k) const {
        mint<MOD> x = *this, y = 1;
        for (; k; k >>= 1) {
            if (k & 1) y *= x;
            x *= x;
        }
        return y;
    }
    mint<MOD> inv() const {
        assert (value != 0);
        int64_t a = value, b = MOD;
        int64_t x = 0, y = 1;
        for (int64_t u = 1, v = 0; a; ) {
            int64_t q = b / a;
            x -= q * u; std::swap(x, u);
            y -= q * v; std::swap(y, v);
            b -= q * a; std::swap(b, a);
        }
        assert (value * x + MOD * y == b);
        assert (b == 1);
        return x;
    }
    inline mint<MOD> operator /  (mint<MOD> other) const { return *this *  other.inv(); }
    inline mint<MOD> operator /= (mint<MOD> other)       { return *this *= other.inv(); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
};
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
template <int32_t MOD>
mint<MOD> fact(int n) {
    static std::vector<mint<MOD> > memo(1, 1);
    while (n >= memo.size()) {
        memo.push_back(memo.back() * mint<MOD>(memo.size()));
    }
    return memo[n];
}
template <int32_t PRIME>
mint<PRIME> inv_fact(int n) {
    static std::vector<mint<PRIME> > memo;
    if (memo.size() <= n) {
        int l = memo.size();
        int r = n * 1.3 + 100;
        memo.resize(r);
        memo[r - 1] = fact<PRIME>(r - 1).inv();
        for (int i = r - 2; i >= l; -- i) {
            memo[i] = memo[i + 1] * (i + 1);
        }
    }
    return memo[n];
}
template <int32_t MOD>
mint<MOD> choose(int n, int r) {
    assert (0 <= r and r <= n);
    return fact<MOD>(n) * inv_fact<MOD>(n - r) * inv_fact<MOD>(r);
}
constexpr int MOD = 1e9 + 7;
mint<MOD> solve(int a, int b, int c) {
    mint<MOD> acc = 0;
    // REP(i, a + b + c - 1) {
    //     REP3(k, 1, a + 1) if (k + 1 <= a + b + c - i - 1) {
    //         acc += mint<MOD>(2).pow(i) * choose<MOD>((a - k) + (b - 1) + (c - 1), (a - k) + (b - 1)) * choose<MOD>((a - k) + (b - 1), a - k);
    //     }
    // }
    REP3(k, 1, a + 1) {
        mint<MOD> x = mint<MOD>(2).pow(a + b + c - k - 1) - 1;
        mint<MOD> y = choose<MOD>((a - k) + (b - 1) + (c - 1), (a - k) + (b - 1)) * choose<MOD>((a - k) + (b - 1), a - k);
        acc += x * y;
    }
    return acc;
}
int main() {
    int a, b, c; cin >> a >> b >> c;
    cout << solve(a, b, c) << endl;
    return 0;
}
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