結果

問題 No.823 Many Shifts Easy
ユーザー kimiyuki
提出日時 2019-04-26 23:53:46
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 28 ms / 2,000 ms
コード長 3,714 bytes
コンパイル時間 2,180 ms
コンパイル使用メモリ 198,552 KB
最終ジャッジ日時 2025-01-07 03:15:12
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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ファイルパターン 結果
other AC * 10
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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) begin(x), end(x)
using namespace std;
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() = default;
    mint(int32_t value_) : value(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 { return pow(MOD - 2); }  // MOD must be a prime
    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> mint<MOD> operator * (int32_t value, mint<MOD> n) { return mint<MOD>(value % MOD) * n; }
template <int32_t MOD> ostream & operator << (ostream & out, mint<MOD> n) { return out << n.value; }
template <int32_t MOD>
mint<MOD> fact(int n) {
    static 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 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);
}
template <int32_t MOD>
mint<MOD> permute(int n, int r) {
    assert (0 <= r and r <= n);
    return fact<MOD>(n) * inv_fact<MOD>(n - r);
}
constexpr int MOD = 1e9 + 7;
mint<MOD> solve(int n, int k) {
    mint<MOD> ans = 0;
    REP (i, n + 1) {
        mint<MOD> a = (mint<MOD>(1) - mint<MOD>(k) / mint<MOD>(n)) * permute<MOD>(n, k);
        mint<MOD> b = (i == n or k == 1) ? 0 : choose<MOD>(k, 2) * permute<MOD>(n - 2, k - 2);
        ans += i * (a + b);
    }
    return ans;
}
int main() {
    int n, k; cin >> n >> k;
    cout << solve(n, k).value << endl;
    return 0;
}
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