#define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long double ld; typedef long long ll; typedef vector vint; typedef pair pii; typedef pair pll; typedef pair pdd; typedef complex compd; #define quickIO() {cin.tie(0); cout.sync_with_stdio(false);} #define reach(i,a) for(auto i:a) #define rep(i,n) for(int i=0;i<(int)n;i++) #define REP(i,n) for(int i=0;i<=(int)n;i++) #define srep(i,a,n) for(int i=a;i<(int)n;i++) #define SREP(i,a,n) for(int i=a;i<=(int)n;i++) #define rrep(i,n) for(int i=n-1;i>=0;i--) #define RREP(i,n) for(int i=n;i>=0;i--) #define all(a) (a).begin(),(a).end() #define mp(a,b) make_pair(a,b) #define mt make_tuple #define pb push_back #define fst first #define scn second int bitcnt(ll x) { x = ((x & 0xAAAAAAAAAAAAAAAA) >> 1) + (x & 0x5555555555555555); x = ((x & 0xCCCCCCCCCCCCCCCC) >> 2) + (x & 0x3333333333333333); x = ((x & 0xF0F0F0F0F0F0F0F0) >> 4) + (x & 0x0F0F0F0F0F0F0F0F); x = ((x & 0xFF00FF00FF00FF00) >> 8) + (x & 0x00FF00FF00FF00FF); x = ((x & 0xFFFF0000FFFF0000) >> 16) + (x & 0x0000FFFF0000FFFF); x = ((x & 0xFFFFFFFF00000000) >> 32) + (x & 0x00000000FFFFFFFF); return x; } int bitcnt(int x) { x = ((x & 0xAAAAAAAA) >> 1) + (x & 0x55555555); x = ((x & 0xCCCCCCCC) >> 2) + (x & 0x33333333); x = ((x & 0xF0F0F0F0) >> 4) + (x & 0x0F0F0F0F); x = ((x & 0xFF00FF00) >> 8) + (x & 0x00FF00FF); x = ((x & 0xFFFF0000) >> 16) + (x & 0x0000FFFF); return x; } ll gcd(ll a, ll b) { return a%b == 0 ? b : gcd(b, a%b); } #define debug(x) cout<<"case #" << x << ": " << endl #define DEBUG 0 const ll inf = 1e18; const ll mod = 1e9 + 7; const ld eps = 1e-15; const int dx[] = { 1,0,-1,0,0 }; const int dy[] = { 0,1,0,-1,0 }; // 1^x+2^x+...+n^x ll dp[10010]; // xの逆元 ll inv[10010]; // x! ll fac[10010]; // x!の逆元 ll invfac[10010]; ll modpow(ll x,ll m) { x %= mod; if (x) { ll ret = 1; while (m) { if (m & 1) ret = (ret*x) % mod; x = (x*x) % mod; m >>= 1; } return ret; } return 0; } ll nCm(int n, int m) { return (fac[n] * ((invfac[n - m] * invfac[m]) % mod)) % mod; } int main() { ll n, k; cin >> n >> k; inv[0] = inv[1] = fac[0] = fac[1] = invfac[0] = invfac[1] = 1; SREP(i, 2, k + 1) { inv[i] = modpow(i,mod-2); fac[i] = (i*fac[i - 1]) % mod; invfac[i] = (inv[i] * invfac[i - 1]) % mod; } dp[0] = n%mod; SREP(i, 1, k) { ll nxt = modpow(n, i + 1); rep(j, i) { nxt += mod + ((i + j + 1) & 1 ? -1 : 1)*((nCm(i + 1, j)*dp[j]) % mod); nxt %= mod; } dp[i] = (nxt*inv[i + 1]) % mod; } cout << dp[k] << endl; return 0; }