結果

問題 No.1035 Color Box
ユーザー r1933r1933
提出日時 2020-04-24 22:37:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 50 ms / 2,000 ms
コード長 7,046 bytes
コンパイル時間 2,234 ms
コンパイル使用メモリ 196,692 KB
最終ジャッジ日時 2025-01-10 00:11:52
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 2
other AC * 36
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 "bits/stdc++.h"

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) x.begin(), x.end()
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define reps(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__)

constexpr size_t    operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t  operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head&& head, Tail&&... tail) {
    cin >> head;
    input(forward<Tail>(tail)...);
}

template <class T>
inline istream& operator>>(istream &is, vector<T> &vec) {
    for (auto &e: vec) {
        is >> e;
    }
    return is;
}

inline void output() { cout << "\n"; }
template <class Head, class... Tail>
inline void output(Head&& head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) {
        cout << " ";
    }
    output(forward<Tail>(tail)...);
}

template <class T>
inline ostream& operator<<(ostream &os, const vector<T> &vec) {
    static constexpr const char *delim[] = {" ", ""};
    for (const auto &e: vec) {
        os << e << delim[&e == &vec.back()];
    }
    return os;
}

template <class T>
inline vector<T> makeVector(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto makeVector(const T &initValue, size_t sz, Args... args) {
    return vector<decltype(makeVector<T>(initValue, args...))>(sz, makeVector<T>(initValue, args...));
}

template <class Func>
class FixPoint : Func {
public:
    explicit constexpr FixPoint(Func&& f) noexcept : Func(forward<Func>(f)) {}

    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return Func::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept {
    return FixPoint<Func>{forward<Func>(f)};
}

template <class Container>
struct reverse_t {
    Container &c;
    reverse_t(Container &c) : c(c) {}
    auto begin() { return c.rbegin(); }
    auto end() { return c.rend(); }
};

template <class Container>
auto reversed(Container &c) {
    return reverse_t<Container>(c);
}

template <class T>
inline bool chmax(T &a, const T &b) noexcept {
    return b > a && (a = b, true);
}

template <class T>
inline bool chmin(T &a, const T &b) noexcept {
    return b < a && (a = b, true);
}

template <class T>
inline T diff(const T &a, const T &b) noexcept {
    return a < b ? b - a : a - b;
}
// End Header }}}

const intmax_t MOD = intmax_t(1e9) + 7;

// ModInt {{{
template <intmax_t MOD>
class ModInt {
    intmax_t value;

public:
    inline ModInt(const ModInt& other) :
        value(other.value)
    {}

    inline ModInt(intmax_t value = 0) {
        if (value >= MOD) {
            this->value = value % MOD;
        } else if (value < 0) {
            this->value = (value + MOD) % MOD;
        } else {
            this->value = value;
        }
    }

    template <class T>
        explicit inline operator T() const {
            return static_cast<T>(value);
        }

    inline ModInt inverse() const {
        return ModInt::pow(value, MOD - 2);
    }

    inline ModInt& operator+=(const ModInt other) {
        value = (value + other.value) % MOD;
        return *this;
    }

    inline ModInt& operator-=(const ModInt other) {
        value = (MOD + value - other.value) % MOD;
        return *this;
    }

    inline ModInt& operator*=(const ModInt other) {
        value = (value * other.value) % MOD;
        return *this;
    }

    inline ModInt& operator/=(const ModInt other) {
        value = (value * other.inverse().value) % MOD;
        return *this;
    }

    inline ModInt operator+(const ModInt other) {
        return ModInt(*this) += other;
    }

    inline ModInt operator-(const ModInt other) {
        return ModInt(*this) -= other;
    }

    inline ModInt operator*(const ModInt other) {
        return ModInt(*this) *= other;
    }

    inline ModInt operator/(const ModInt other) {
        return ModInt(*this) /= other;
    }

    inline bool operator==(const ModInt other) {
        return value == other.value;
    }

    inline bool operator!=(const ModInt other) {
        return value != other.value;
    }

    friend ostream& operator<<(ostream &os, const ModInt other) {
        os << other.value;
        return os;
    }

    friend istream& operator>>(istream &is, ModInt& other) {
        is >> other.value;
        return is;
    }

    static constexpr inline ModInt pow(intmax_t n, intmax_t p) {
        intmax_t ret = 1;
        for (; p > 0; p >>= 1) {
            if (p & 1) ret = (ret * n) % MOD;
            n = (n * n) % MOD;
        }
        return ret;
    }
};

using Mint = ModInt<MOD>;
// }}}

// Factorial {{{
#ifdef DEBUG
#define constexpr
#endif

template <size_t N, size_t MOD>
struct Factorial {
    vector<uint_fast64_t> fact_;

    constexpr inline Factorial() : fact_(N + 1) {
        fact_[0] = 1;
        for (intmax_t i = 1; i <= N; ++i) {
            fact_[i] = (fact_[i - 1] * i) % MOD;
        }
    }

    constexpr inline Mint operator[](size_t pos) const {
        return fact_[pos];
    }
};

template <size_t N, size_t MOD>
struct InvFact {
    vector<uint_fast64_t> inv_;
    vector<uint_fast64_t> finv_;

    constexpr inline InvFact() : inv_(N + 1), finv_(N + 1) {
        inv_[1] = 1;
        finv_[0] = finv_[1] = 1;
        for (intmax_t i = 2; i <= N; ++i) {
            inv_[i] = (MOD - MOD / i) * inv_[MOD % i] % MOD;
            finv_[i] = finv_[i - 1] * inv_[i] % MOD;
        }
    }

    constexpr inline Mint operator[](size_t pos) const {
        return finv_[pos];
    }
};

#ifdef constexpr
#undef constexpr
#endif

Factorial<510000, MOD> fact;
InvFact<510000, MOD> finv;

inline Mint nCr(int n, int r) {
    if (r < 0 || n < r) {
        return 0;
    }
    return fact[n] * (finv[r] * finv[n - r]);
}

inline Mint nPr(int n, int r) {
    if (r < 0 || n < r) {
        return 0;
    }
    return fact[n] * finv[n - r];
}

inline Mint nHr(int n, int r) {
    return nCr(n + r - 1, r);
}
// }}}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.setf(ios_base::fixed);
    cout.precision(10);
    var(intmax_t, N, M);
    Mint res = Mint::pow(M, N);
    Mint m = 0;
    rep(i, 1, M) {
        m = nCr(M, i) * Mint::pow(i, N) - m;
    }
    output(res - m);
    return 0;
}
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