#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef _WIN64 # include #endif #ifdef _MSC_VER # include # define __builtin_popcount __popcnt # define __builtin_popcountl __popcnt64 #endif using namespace std; #define ll long long #define rep(i, init, n) for(ll i = init; i < (ll)n; i++) #define rrep(i, init, n) for(ll i = init; i >= (ll)n; i--) #define all(x) (x).begin(), (x).end() #define sz(x) (ll)(x.size()) #define Out(x) cout << x << endl #define Yes cout << "Yes" << endl #define No cout << "No" << endl #define Ans cout << ans << endl #define PI 3.14159265358979 #define MOD 1000000007 const int inf32 = INT_MAX / 2; const ll inf64 = 1LL << 60; templatebool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } templatebool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } return false; } // ------------------------------------------------------------------------------------------------- struct mint { ll x; mint(ll val = 0) { x = (val % MOD + MOD) % MOD; } mint operator-() const { return mint(-x); } mint& operator+=(const mint& other) { x += other.x; if (x >= MOD) x -= MOD; return *this; } mint& operator-=(const mint& other) { x -= other.x; if (x < 0) x += MOD; return *this; } mint& operator*=(const mint& other) { (x *= other.x) %= MOD; return *this; } mint& operator/=(const mint& other) { *this *= other.pow(MOD - 2); return *this; } mint operator+(const mint& other) const { return mint(*this) += other; } mint operator-(const mint& other) const { return mint(*this) -= other; } mint operator*(const mint& other) const { return mint(*this) *= other; } mint operator/(const mint& other) const { return mint(*this) /= other; } mint pow(ll i) const { mint ret = 1; for (mint tmp = x; i; tmp *= tmp, i >>= 1) if (i & 1) ret *= tmp; return ret; } friend ostream& operator<<(ostream& os, const mint& m) { os << m.x; return os; } }; struct Combination { vector f, finv; bool precalc = false; Combination(ll n, bool calc_inv = false) { f.resize(n + 1); if (calc_inv) finv.resize(n + 1), precalc = true; f[0] = 1; rep(i, 1, n + 1) f[i] = f[i - 1] * i % MOD; if (calc_inv) rep(i, 0, n + 1) finv[i] = mpow(f[i], MOD - 2); } ll mpow(ll x, ll y) { if (y == 0) return 1; x %= MOD; if (x == 0) return 0; if (y % 2 == 0) return mpow(x * x % MOD, y / 2) % MOD; else return x * mpow(x, y - 1) % MOD; } ll P(ll x, ll y) { return precalc ? f[x] * finv[x - y] % MOD : f[x] * mpow(f[x - y], MOD - 2) % MOD; } ll C(ll x, ll y) { ll a = f[x]; ll b = precalc ? finv[y] * finv[x - y] % MOD : mpow(f[y] * f[x - y] % MOD, MOD - 2); return a * b % MOD; } ll H(ll x, ll y) { return C(x + y - 1, y); } }; ll mpow(ll x, ll y) { if (y == 0) return 1; x %= MOD; if (x == 0) return 0; if (y % 2 == 0) return mpow(x * x % MOD, y / 2) % MOD; else return x * mpow(x, y - 1) % MOD; } int main() { ll n, m; cin >> n >> m; Combination comb(100000, true); mint ans = mpow(m, n); rep(i, 1, m) { mint tmp = (mint)comb.C(m, i) * mpow(i, n); ans += tmp * ((m - i) % 2 != 0 ? -1 : 1); } Ans; return 0; }