Verify/combination.test.cpp

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Last update: 2021-04-20 01:42:38+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/courses/library/7/DPL/all/DPL_5_C

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/7/DPL/all/DPL_5_C"

#include "../Number/modint.hpp"
#include "../Number/combination.hpp"

constexpr int MOD = 1e9 + 7;
using mint = ModInt<MOD>;

const Combination<mint> C(1000);

int main() {
    std::cin.tie();
    std::ios::sync_with_stdio(false);

    int n, k;
    std::cin >> n >> k;

    mint ans = 0;
    for (int i = 0; i <= k; ++i) {
        ans += mint(-1).pow(k - i) * C.binom(k, i) * mint(i).pow(n);
    }
    std::cout << ans << "\n";

    return 0;
}

#line 1 "Verify/combination.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/7/DPL/all/DPL_5_C"

#line 2 "Number/modint.hpp"

#include <iostream>

template <int MOD>
struct ModInt {
    using lint = long long;
    int val;

    // constructor
    ModInt(lint v = 0) : val(v % MOD) {
        if (val < 0) val += MOD;
    };

    // unary operator
    ModInt operator+() const { return ModInt(val); }
    ModInt operator-() const { return ModInt(MOD - val); }

    ModInt& operator++() { return *this += 1; }
    ModInt& operator--() { return *this -= 1; }

    // functions
    ModInt pow(lint n) const {
        auto x = ModInt(1);
        auto b = *this;
        while (n > 0) {
            if (n & 1) x *= b;
            n >>= 1;
            b *= b;
        }
        return x;
    }
    ModInt inv() const {
        int s = val, t = MOD,
            xs = 1, xt = 0;

        while (t != 0) {
            auto div = s / t;

            s -= t * div;
            xs -= xt * div;

            std::swap(s, t);
            std::swap(xs, xt);
        }

        return xs;
    }

    // arithmetic
    ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
    ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
    ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
    ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }

    ModInt& operator+=(const ModInt& x) {
        if ((val += x.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt& x) {
        if ((val -= x.val) < 0) val += MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt& x) {
        val = lint(val) * x.val % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }

    // comparator
    bool operator==(const ModInt& b) const { return val == b.val; }
    bool operator!=(const ModInt& b) const { return val != b.val; }

    // I/O
    friend std::istream& operator>>(std::istream& is, ModInt& x) {
        lint v;
        is >> v;
        x = v;
        return is;
    }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) {
        return os << x.val;
    }
};

using modint1000000007 = ModInt<1000000007>;
using modint998244353 = ModInt<998244353>;
#line 2 "Number/combination.hpp"

#include <vector>

template <class T>
struct Combination {
    int max_n;
    std::vector<T> f, invf;

    explicit Combination(int n)
        : max_n(n), f(n + 1), invf(n + 1) {
        f[0] = 1;
        for (int i = 1; i <= n; ++i) {
            f[i] = f[i - 1] * i;
        }

        invf[max_n] = f[max_n].inv();
        for (int i = max_n - 1; i >= 0; --i) {
            invf[i] = invf[i + 1] * (i + 1);
        }
    }

    T fact(int n) const { return n < 0 ? T(0) : f[n]; }
    T invfact(int n) const { return n < 0 ? T(0) : invf[n]; }
    T perm(int a, int b) const {
        return a < b || b < 0 ? T(0) : f[a] * invf[a - b];
    }
    T binom(int a, int b) const {
        return a < b || b < 0 ? T(0) : f[a] * invf[a - b] * invf[b];
    }
};
#line 5 "Verify/combination.test.cpp"

constexpr int MOD = 1e9 + 7;
using mint = ModInt<MOD>;

const Combination<mint> C(1000);

int main() {
    std::cin.tie();
    std::ios::sync_with_stdio(false);

    int n, k;
    std::cin >> n >> k;

    mint ans = 0;
    for (int i = 0; i <= k; ++i) {
        ans += mint(-1).pow(k - i) * C.binom(k, i) * mint(i).pow(n);
    }
    std::cout << ans << "\n";

    return 0;
}