結果

問題 No.1035 Color Box
ユーザー tkmst201
提出日時 2021-02-19 21:49:13
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 14 ms / 2,000 ms
コード長 5,043 bytes
コンパイル時間 2,016 ms
コンパイル使用メモリ 198,524 KB
最終ジャッジ日時 2025-01-18 23:46:01
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 36
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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>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = false;
//---------------------------------//
template<int M>
struct ModInt {
    static_assert(M > 0);
    
public:
    using value_type = int;
    using calc_type = std::int_fast64_t;
    
private:
    value_type val_;
    
public:
    constexpr ModInt(calc_type val = 0) : val_(val < 0 ? (val % M + M) % M : val % M) {}
    constexpr const value_type & val() const noexcept { return val_; }
    constexpr static decltype(M) mod() noexcept { return M; }
    
    explicit constexpr operator bool() const noexcept { return val_; }
    constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
    constexpr ModInt operator +() const noexcept { return ModInt(*this); }
    constexpr ModInt operator -() const noexcept { return ModInt(-val_); }
    constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
    constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
    constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
    constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
    constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
    constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
    constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
    constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
    friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
    friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
    friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
    friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
    friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
    
    constexpr ModInt pow(calc_type n) const noexcept {
        ModInt res = 1, x = val_;
        if (n < 0) { x = x.inv(); n = -n; }
        while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
        return res;
    }
    
    constexpr ModInt inv() const noexcept {
        value_type a = val_, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;
        while (b > 0) {
            value_type q = a / b, r = a % b;
            value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;
            a = b; b = r;
            a1 = b1; b1 = nb1;
            a2 = b2; b2 = nb2;
        }
        assert(a == 1);
        return a1;
    }
};
using mint = ModInt<MOD>;
template<typename T>
struct Combination {
public:
    using size_type = std::size_t;
    
    Combination(size_type sz = 1) : fact_(1, 1), finv_(1, 1), inv_(1, 1) { build(sz); }
    
    T fact(size_type k) { if (k >= T::mod()) return 0; build(k); return fact_[k]; }
    T finv(size_type k) { assert(k < T::mod()); build(k); return finv_[k]; }
    T inv(size_type k) { assert(k > 0 && k < T::mod()); build(k); return inv_[k]; }
    
    T operator ()(int n, int r) { return c(n, r); }
    T c(int n, int r) {
        if (r < 0 || n < r) return 0;
        return fact(n) * finv(r) * finv(n - r);
    }
    
private:
    std::vector<T> fact_, finv_, inv_;
    static constexpr size_type MAX_LIMIT = 50000000;
    
    void build(size_type k) {
        if (fact_.size() > k) return;
        assert(k < MAX_LIMIT);
        size_type sz = std::min({MAX_LIMIT, static_cast<size_type>(T::mod()), std::max(fact_.size() * 2, k + 1)});
        size_type presz = fact_.size();
        fact_.resize(sz);
        finv_.resize(sz);
        inv_.resize(sz);
        
        for (size_type i = presz; i < sz; ++i) fact_[i] = fact_[i - 1] * i;
        finv_[sz - 1] = T(fact_[sz - 1]).inv();
        for (size_type i = sz - 1; i > presz; --i) {
            finv_[i - 1] = finv_[i] * i;
            inv_[i] = fact_[i - 1] * finv_[i];
        }
        inv_[presz] = fact_[presz - 1] * finv_[presz];
    }
};
using Comb = Combination<mint>;
Comb comb;
int main() {
    int N, M;
    cin >> N >> M;
    mint ans = 0;
    REP(i, M + 1) {
        mint cur = comb(M, i) * mint(M - i).pow(N);
        ans += cur * (i & 1 ? -1 : 1);
    }
    cout << ans << endl;
}
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