#line 1 "main.cpp" #include #line 2 "/home/user/GitHub/competitive-programming-library/utils/macros.hpp" #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) #line 3 "/home/user/GitHub/competitive-programming-library/modulus/modpow.hpp" inline constexpr int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) { assert (0 <= x and x < MOD); uint_fast64_t y = 1; for (; k; k >>= 1) { if (k & 1) (y *= x) %= MOD; (x *= x) %= MOD; } assert (0 <= y and y < MOD); return y; } #line 4 "/home/user/GitHub/competitive-programming-library/modulus/modinv.hpp" inline int32_t modinv_nocheck(int32_t value, int32_t MOD) { assert (0 <= value and value < MOD); if (value == 0) return -1; 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); } if (not (value * x + MOD * y == b and b == 1)) return -1; if (x < 0) x += MOD; assert (0 <= x and x < MOD); return x; } inline int32_t modinv(int32_t x, int32_t MOD) { int32_t y = modinv_nocheck(x, MOD); assert (y != -1); return y; } #line 7 "/home/user/GitHub/competitive-programming-library/modulus/mint.hpp" /** * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$ */ template struct mint { int32_t value; mint() : value() {} mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {} mint(int32_t value_, std::nullptr_t) : value(value_) {} explicit operator bool() const { return value; } inline constexpr mint operator + (mint other) const { return mint(*this) += other; } inline constexpr mint operator - (mint other) const { return mint(*this) -= other; } inline constexpr mint operator * (mint other) const { return mint(*this) *= other; } inline constexpr mint & operator += (mint other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; } inline constexpr mint & operator -= (mint other) { this->value -= other.value; if (this->value < 0) this->value += MOD; return *this; } inline constexpr mint & operator *= (mint other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; } inline constexpr mint operator - () const { return mint(this->value ? MOD - this->value : 0, nullptr); } inline constexpr mint pow(uint64_t k) const { return mint(modpow(value, k, MOD), nullptr); } inline mint inv() const { return mint(modinv(value, MOD), nullptr); } inline constexpr mint operator / (mint other) const { return *this * other.inv(); } inline constexpr mint operator /= (mint other) { return *this *= other.inv(); } inline constexpr bool operator == (mint other) const { return value == other.value; } inline constexpr bool operator != (mint other) const { return value != other.value; } }; template mint operator * (int64_t value, mint n) { return mint(value) * n; } template std::istream & operator >> (std::istream & in, mint & n) { int64_t value; in >> value; n = value; return in; } template std::ostream & operator << (std::ostream & out, mint n) { return out << n.value; } #line 4 "/home/user/GitHub/competitive-programming-library/modulus/factorial.hpp" template mint fact(int n) { static std::vector > memo(1, 1); while (n >= memo.size()) { memo.push_back(memo.back() * mint(memo.size())); } return memo[n]; } template mint inv_fact(int n) { static std::vector > memo; if (memo.size() <= n) { int l = memo.size(); int r = n * 1.3 + 100; memo.resize(r); memo[r - 1] = fact(r - 1).inv(); for (int i = r - 2; i >= l; -- i) { memo[i] = memo[i + 1] * (i + 1); } } return memo[n]; } #line 5 "/home/user/GitHub/competitive-programming-library/modulus/choose.hpp" /** * @brief combination / 組合せ ${} _ n C _ r$ (前処理 $O(n)$ + $O(1)$) */ template mint choose(int n, int r) { assert (0 <= r and r <= n); return fact(n) * inv_fact(n - r) * inv_fact(r); } #line 5 "main.cpp" using namespace std; constexpr int64_t MOD = 1000000007; mint solve(int n, int m) { mint ans = 0; REP (i, m + 1) { int sign = (i % 2 == 0 ? 1 : -1); ans += sign * choose(m, m - i) * mint(m - i).pow(n); } return ans; } // generated by online-judge-template-generator v4.1.0 (https://github.com/kmyk/online-judge-template-generator) int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); constexpr char endl = '\n'; int N, M; cin >> N >> M; auto ans = solve(N, M); cout << ans << endl; return 0; }