#include #define debug(x) cerr << #x << ": " << x << endl #define debugArray(x, n) \ for (long long hoge = 0; (hoge) < (n); ++(hoge)) \ cerr << #x << "[" << hoge << "]: " << x[hoge] << endl using namespace std; template struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod)) {} ModInt &operator+=(const ModInt &p) { if ((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int)(1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { return *this *= p.inverse(); } ModInt operator-() const { return ModInt() - *this; } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while (b) t = a / b, swap(a -= t * b, b), swap(u -= t * v, v); return ModInt(u); } ModInt pow(int64_t e) const { ModInt ret(1); for (ModInt b = *this; e; e >>= 1, b *= b) if (e & 1) ret *= b; return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt(t); return (is); } static int modulo() { return mod; } }; template struct Combination { static vector _fact, _finv, _inv; static void init(int sz) { int n = min(sz, Modint::modulo() - 1); _fact.resize(n + 1), _finv.resize(n + 1), _inv.resize(n + 1); for (int i = 0; i <= n; ++i) _fact[i] = i ? Modint(i) * _fact[i - 1] : 1; _finv[n] = _fact[n].inverse(); for (int i = n; i; --i) _finv[i - 1] = Modint(i) * _finv[i]; for (int i = 1; i <= n; ++i) _inv[i] = _finv[i] * _fact[i - 1]; } static Modint inverse(int n) { return _inv[n]; } static Modint fact(int n, bool inv = 0) { return inv ? _finv[n] : _fact[n]; } static Modint nPr(int n, int r) { if (n < r || r < 0) return Modint(0); return _fact[n] * _finv[n - r]; } static Modint nCr(int n, int r) { return nPr(n, r) * _finv[r]; } static Modint nHr(int n, int r) { return !r ? Modint(1) : nCr(n + r - 1, r); } static size_t size() { return _inv.size(); } }; template vector Combination::_fact; template vector Combination::_finv; template vector Combination::_inv; signed main() { cin.tie(0); ios::sync_with_stdio(false); using Mint = ModInt<(int)1e9 + 7>; using Comb = Combination; int N, M; cin >> N >> M; Comb::init(M); Mint ans = 0; for (int i = 1; i <= M; i++) { Mint tmp = Mint(i).pow(N) * Comb::nCr(M, i); if ((M - i) & 1) ans -= tmp; else ans += tmp; } cout << ans << endl; return 0; }