#include #define int long long #define lint long long #define pii pair #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define REP(i,n) FOR(i,0,n) #define ALL(c) (c).begin(),(c).end() #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) #define MINF(a) memset(a,0x3f,sizeof(a)) #define POW(n) (1LL<<(n)) #define POPCNT(n) (__builtin_popcount(n)) #define IN(i,a,b) (a <= i && i <= b) using namespace std; template inline bool CHMIN(T& a,T b) { if(a>b) { a=b; return 1; } return 0; } template inline bool CHMAX(T& a,T b) { if(a inline void SORT(T& a) { sort(ALL(a)); } template inline void REV(T& a) { reverse(ALL(a)); } template inline void UNI(T& a) { sort(ALL(a)); a.erase(unique(ALL(a)),a.end()); } template inline T LB(vector& v, T a) { return *lower_bound(ALL(v),a); } template inline int LBP(vector& v, T a) { return lower_bound(ALL(v),a) - v.begin(); } template inline T UB(vector& v, T a) { return *upper_bound(ALL(v),a); } template inline int UBP(vector& v, T a) { return upper_bound(ALL(v),a) - v.begin(); } template ostream& operator<< (ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template istream& operator>> (istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<< (ostream& os, const vector& v) { REP(i,v.size()) { if (i) os << " "; os << v[i]; } return os; } template istream& operator>> (istream& is, vector& v) { for(T& in : v) is >> in; return is; } template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a,make_v(ts...)); } template typename enable_if::value == 0>::type fill_v(T &t, const V &v) { t = v; } template typename enable_if::value != 0>::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e,v); } const lint MOD = 1000000007; const lint INF = 0x3f3f3f3f3f3f3f3f; const double EPS = 1e-10; const int MAX = 100010; long long inv[MAX]; long long fac[MAX]; long long finv[MAX]; void init() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (long long i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } // 累乗 a^n long long pow_mod(long long a, long long n) { long long res = 1; while (n > 0) { if (n & 1) res = res * a % MOD; a = a * a % MOD; n >>= 1; } return res; } // nCk (階乗 + 逆元) // n < 10^7, k < 10^7, n,k < MOD, MOD: 素数 // 前計算 O(n) 時間 // 本計算 O(1) 時間 long long nCk(int n, int k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * finv[k] % MOD * finv[n - k] % MOD; } // 包除原理 (n: 玉の数, k: 箱の数) // O(k log n) long long PIE(int n, int k) { if (k > n) return 0; if (n < 0 || k < 0) return 0; long long res = 0; for (int i = 0; i <= k; i++) { long long tmp = nCk(k, i) * pow_mod(i, n) % MOD; if ((k - i) & 1) res = (res + MOD - tmp) % MOD; else res = (res + tmp) % MOD; } return res; } void _main() { init(); int N, M; cin >> N >> M; cout << PIE(N, M) << endl; } signed main(signed argc, char **argv) { if (argc > 1) { if (strchr(argv[1], 'i')) freopen("input.txt", "r", stdin); if (strchr(argv[1], 'o')) freopen("output.txt", "w", stdout); } cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); _main(); return 0; }