#ifdef LOCAL111 #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #define _USE_MATH_DEFINES #ifndef _GLIBCXX_NO_ASSERT #include #endif #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #if __cplusplus >= 201103L #include #include #include #include #include #include #include #include #endif // C++ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #if __cplusplus >= 201103L #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #endif const int INF = 1e9; using namespace std; template ostream& operator<< (ostream& os, const pair& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; } #define endl '\n' #define ALL(a) (a).begin(),(a).end() #define SZ(a) int((a).size()) #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) for (int i=(n)-1;i>=0;i--) #ifdef LOCAL111 #define DEBUG(x) cout<<#x<<": "<<(x)< void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} #else #define DEBUG(x) true template void dpite(T a, T b){ return; } #endif #define F first #define S second #define SNP string::npos #define WRC(hoge) cout << "Case #" << (hoge)+1 << ": " template void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} template bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;} template bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;} typedef long long int LL; typedef unsigned long long ULL; typedef pair P; void ios_init(){ //cout.setf(ios::fixed); //cout.precision(12); #ifdef LOCAL111 return; #endif ios::sync_with_stdio(false); cin.tie(0); } template class ModInt { public: const static long long mod = MOD; long long x; ModInt() { x = 0; } ModInt(long long x) { x %= mod; this->x = x < 0 ? x+mod : x; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.get()) >= mod) x -= mod; return *this; } ModInt &operator-=(ModInt that) { if((x += mod-that.get()) >= mod) x -= mod; return *this; } ModInt &operator*=(ModInt that) { x = x*that.get()%mod; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { using std::swap; long long a = x, b = mod, u = 1, v = 0; while(b) { long long t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } return ModInt(u); } ModInt pow(int n) const{ ModInt b = *this; ModInt res = 1; while(n != 0) { if(n&1){ res *= b; } b *= b; n >>= 1; } return res; } bool operator==(ModInt that) const { return x == that.get(); } bool operator!=(ModInt that) const { return x != that.get(); } ModInt operator-() const { return x == 0 ? 0 : ModInt(mod-x); } }; template ostream& operator<< (ostream& os, const ModInt& m) { os << m.get(); return os; } template istream& operator>> (istream& is, ModInt& m){ long long n; is >> n; m = n; return is;} typedef ModInt<1000000007> mint; class ConvQuery { vector fac; vector facinv; public: ConvQuery(int n) { fac = vector(n+1); facinv = vector(n+1); fac[0] = 1; facinv[0] = 1; for(int i = 0; i < n; ++i) { fac[i+1] = fac[i]*(i+1); facinv[i+1] = fac[i+1].inverse(); } } mint operator()(int n, int m) { if(n >= 0 and 0 <= m and m <= n) return fac[n]*facinv[n-m]*facinv[m]; else return 0; } }; int main() { ios_init(); LL n, k; while(cin >> n >> k) { vector f(k+2); vector dp(k+2); f[1] = 1; dp[1] = mint(n) * mint(n+1) / 2; mint ka = mint(n) * mint(n+1) / 2; vector inv(k+1); FOR(i, 1, k+1) { inv[i] = mint(i).inverse(); } FOR(i, 2, k+1) { DEBUG(i); mint pre = 0; ka *= n-i+1; ka /= i+1; DEBUG(ka); REP(j, i+2) { mint t = f[j]; f[j] *= -(i-1); f[j] += pre; // f[j] /= i; f[j] *= inv[i]; pre = t; } DEBUG(ka); dpite(ALL(f)); dp[i] = ka; REP(j, i) { dp[i] -= dp[j] * f[j]; } dp[i] /= f[i]; } dpite(ALL(dp)); cout << dp[k] << endl; } return 0; }