# pragma GCC optimize ("O3") # pragma GCC optimize ("Ofast") # pragma GCC optimize ("unroll-loops") #include #pragma warning(disable:4996) #pragma comment(linker, "/STACK:336777216") using namespace std; typedef long long ll; typedef pair pii; typedef vector vi; typedef tuple ti3; typedef tuple ti4; typedef stack si; typedef queue qi; typedef priority_queue pqi; typedef pair pll; typedef vector vl; typedef tuple tl3; typedef tuple tl4; typedef stack sl; typedef queue ql; typedef priority_queue pql; int dx[4] = { 1,-1,0,0 }; int dy[4] = { 0,0,1,-1 }; int ddx[8] = { 0,0,1,1,1,-1,-1,-1 }, ddy[8] = { 1,-1,1,0,-1,1,0,-1 }; ll POW(ll a, ll b, ll MMM) { ll ret = 1; for (; b; b >>= 1, a = (a*a) % MMM)if (b & 1)ret = (ret*a) % MMM; return ret; } ll GCD(ll a, ll b) { return b ? GCD(b, a%b) : a; } ll LCM(ll a, ll b) { if (a == 0 || b == 0)return a + b; return a / GCD(a, b) * b; } ll INV(ll a, ll m) { ll m0 = m, y = 0, x = 1; if (m == 1) return 0; while (a > 1) { ll q = a / m; ll t = m; m = a % m, a = t; t = y; y = x - q * y; x = t; } if (x < 0) x += m0; return x; } pll EXGCD(ll a, ll b) { if (b == 0) return { 1,0 }; auto t = EXGCD(b, a%b); return { t.second,t.first - t.second*(a / b) }; } bool OOB(ll x, ll y, ll N, ll M) { return 0 > x || x >= N || 0 > y || y >= M; } #define X first #define Y second #define rep(i,a,b) for(int i = a; i < b; i++) #define pb push_back #define all(x) (x).begin(), (x).end() #define sz(a) ((int)(a.size())) #define sf1(a) cin >> a #define sf2(a,b) cin >> a >> b #define sf3(a,b,c) cin >> a >> b >> c #define sf4(a,b,c,d) cin >> a >> b >> c >> d #define sf5(a,b,c,d,e) cin >> a >> b >> c >> d >> e #define sf6(a,b,c,d,e,f) cin >> a >> b >> c >> d >> e >> f #define pf1(a) cout << (a) << ' ' #define pf2(a,b) cout << (a) << ' ' << (b) << ' ' #define pf3(a,b,c) cout << (a) << ' ' << (b) << ' '<< (c) << ' ' #define pf4(a,b,c,d) cout << (a) << ' ' << (b) << ' '<< (c) << ' '<< (d) << ' ' #define pf5(a,b,c,d,e) cout << (a) << ' ' << (b) << ' '<< (c) << ' '<< (d) << ' '<< (e) << ' ' #define pf6(a,b,c,d,e,f) cout << (a) << ' ' << (b) << ' '<< (c) << ' '<< (d) << ' '<< (e) << ' ' << (f) << ' ' #define pf0l() cout << '\n'; #define pf1l(a) cout << (a) << '\n' #define pf2l(a,b) cout << (a) << ' ' << (b) << '\n' #define pf3l(a,b,c) cout << (a) << ' ' << (b) << ' '<< (c) << '\n' #define pf4l(a,b,c,d) cout << (a) << ' ' << (b) << ' '<< (c) << ' '<< (d) << '\n' #define pf5l(a,b,c,d,e) cout << (a) << ' ' << (b) << ' '<< (c) << ' '<< (d) << ' '<< (e) << '\n' #define pf6l(a,b,c,d,e,f) cout << (a) << ' ' << (b) << ' '<< (c) << ' '<< (d) << ' '<< (e) << ' ' << (f) << '\n' #define pfvec(V) for(auto const &t : V) pf1(t) #define pfvecl(V) for(auto const &t : V) pf1(t); pf0l() ll combi[10002][10002]; const ll MOD = 1e9 + 7; ll N, K; ll powdiv[10001]; int main(void) { ios::sync_with_stdio(false); cin.tie(0); combi[0][0] = 1; rep(i, 1, 10002) { combi[i][0] = combi[i][i] = 1; rep(j, 1, i) combi[i][j] = (combi[i - 1][j] + combi[i - 1][j - 1]) % MOD; } sf2(N, K); powdiv[0] = N; powdiv[1] = (N*(N + 1) / 2) % MOD; rep(k, 2, K + 1) { powdiv[k] = POW(N + 1, k + 1, MOD)-1; rep(j, 2, k + 2) powdiv[k] = (powdiv[k] - combi[k + 1][j] * powdiv[k - j + 1]) % MOD; powdiv[k] = (powdiv[k] * INV(k + 1, MOD)) % MOD; if (powdiv[k] < 0) powdiv[k] += MOD; } pf1l(powdiv[K]); }