#include #include #include #include #include #include #include #include #include #include #define mkp make_pair #define mkt make_tuple #define rep(i, n) for (int i = 0; i < (n); ++i) #define all(v) v.begin(), v.end() using namespace std; typedef long long ll; const ll MOD = 1e9 + 7; // const ll MOD = 998244353; template void chmin(T& a, const T& b) { if (a > b) a = b; } template void chmax(T& a, const T& b) { if (a < b) a = b; } template class modint { private: using T = long long; T a; public: constexpr modint(const long long x = 0) noexcept : a((x % mod + mod) % mod) {} constexpr T& value() noexcept { return a; } constexpr const T& value() const noexcept { return a; } constexpr modint operator-() const noexcept { return modint(0) -= *this; } constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint& operator+=(const modint& rhs) noexcept { a += rhs.a; if (a >= mod) a -= mod; return *this; } constexpr modint& operator-=(const modint& rhs) noexcept { if (a < rhs.a) a += mod; a -= rhs.a; return *this; } constexpr modint& operator*=(const modint& rhs) noexcept { a = a * rhs.a % mod; return *this; } constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.inv(); } constexpr bool operator==(const modint& rhs) const noexcept { return a == rhs.a; } constexpr bool operator!=(const modint& rhs) const noexcept { return not(*this == rhs); } constexpr modint pow(long long k) const noexcept { modint ret(1); modint x = k > 0 ? *this : this->inv(); k = abs(k); while (k > 0) { if (k & 1) ret *= x; x *= x; k >>= 1; } return ret; } constexpr modint inv() const noexcept { return pow(mod - 2); } friend std::ostream& operator<<(std::ostream& os, const modint& X) noexcept { return os << X.a; } friend std::istream& operator>>(std::istream& is, modint& X) noexcept { is >> X.a; X.a %= mod; if (X.a < 0) X.a += mod; return is; } }; template struct Combination { int MAX_N = 1'000'010; vector fac, ifac, inv; Combination(int MAX_N = 1'000'010) : MAX_N(MAX_N), fac(MAX_N), ifac(MAX_N), inv(MAX_N) { fac[0] = 1, ifac[0] = 1, inv[0] = 1; for (int i = 1; i < MAX_N; ++i) { fac[i] = fac[i - 1] * i; } ifac[MAX_N - 1] = T(1) / fac[MAX_N - 1]; for (int i = MAX_N - 1; i > 0; --i) { ifac[i - 1] = ifac[i] * i; } for (int i = MAX_N - 1; i > 0; --i) { inv[i] = ifac[i] * fac[i - 1]; } } T perm(int n, int k) { if (n < k || n < 0 || k < 0) return 0; else return fac[n] * ifac[n - k]; } T comb(int n, int k) { if (n < k || n < 0 || k < 0) return 0; else return fac[n] * ifac[k] * ifac[n - k]; } T hcomb(int n, int r) { // this size is really ok?? if (n == 0 && r == 0) return 1; else if (n < 0 || r < 0) return 0; else return comb(n + r - 1, r); } T binom(ll _n, int k) { if (_n < k || _n < 0 || k < 0) return 0; T n = _n; T res = 1; for (int i = 0; i < k; i++) res = res * (n - i); res *= ifac[k]; return res; } }; using mint = modint<1000000007>; void solve() { Combination math; int N, M; cin >> N >> M; vector dp(M + 1, 0); for (int i = 1; i <= M; i++) { mint res = math.comb(M, i) * mint(i).pow(N); res -= dp[i - 1]; dp[i] = res; } mint ans = dp[M]; cout << ans << endl; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); solve(); return 0; }