#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) void *wmem; char memarr[96000000]; template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } struct graph{ int N; int *es; int **edge; void setEdge(int N__, int M, int A[], int B[], void **mem = &wmem){ int i; N = N__; walloc1d(&es, N, mem); walloc1d(&edge, N, mem); for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ es[A[i]]++; es[B[i]]++; } for(i=(0);i<(N);i++){ walloc1d(&edge[i], es[i], mem); } for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ edge[A[i]][es[A[i]]++] = B[i]; edge[B[i]][es[B[i]]++] = A[i]; } } void getDist(int root, int res[], void *mem = wmem){ int i; int j; int k; int*q; int s; int z; walloc1d(&q, N, &mem); for(i=(0);i<(N);i++){ res[i]=-1; } res[root]=0; s=0; z=1; q[0]=root; while(z){ i=q[s++]; z--; for(j=(0);j<(es[i]);j++){ k=edge[i][j]; if(res[k]>=0){ continue; } res[k]=res[i]+1; q[s+z++]=k; } } } } ; int N; int K; int A[1000]; int B[1000]; graph g; Modint res; int up[1000]; int d[1000]; int vis[1000][1000]; Modint dp[1000][1000]; Modint solve(int n, int k){ int Lj4PdHRW; Modint res = 1; if(k<0){ return 0; } if(vis[n][k]){ return dp[n][k]; } vis[n][k] = 1; for(Lj4PdHRW=(0);Lj4PdHRW<(g.es[n]);Lj4PdHRW++){ auto &i = g.edge[n][Lj4PdHRW]; if(i==up[n]){ continue; } res *= solve(i,k); } res += solve(n,k-1); return dp[n][k] = res; } Modint dp2[1000][1000]; void dfs(int n){ int xr20shxY; if(up[n]==-1){ dp2[n][0] = 1; res += dp[n][K-1]; } else{ int i; Modint s = 0; Modint t; for(i=(0);i<(K);i++){ if(i){ t = dp[up[n]][i] -dp[up[n]][i-1]; } else{ t = dp[up[n]][i] -0; } t /= dp[n][i]; s += dp2[up[n]][i]; dp2[n][i] = t * s; } s = 0; for(i=(1);i<(K);i++){ s += dp2[n][i-1]; res += (dp[n][i]-dp[n][i-1]) * s; } } for(xr20shxY=(0);xr20shxY<(g.es[n]);xr20shxY++){ auto &i = g.edge[n][xr20shxY]; if(i==up[n]){ continue; } dfs(i); } } int main(){ int i; wmem = memarr; rd(N); rd(K); { int KrdatlYV; for(KrdatlYV=(0);KrdatlYV<(N-1);KrdatlYV++){ rd(A[KrdatlYV]);A[KrdatlYV] += (-1); rd(B[KrdatlYV]);B[KrdatlYV] += (-1); } } g.setEdge(N,N-1,A,B); g.getDist(0, d); up[0] = -1; for(i=(0);i<(N);i++){ int V9aVTaxx; for(V9aVTaxx=(0);V9aVTaxx<(g.es[i]);V9aVTaxx++){ auto &j = g.edge[i][V9aVTaxx]; if(d[j]==d[i]-1){ up[i] = j; } } } solve(0, K-1); dfs(0); wt_L(res); wt_L('\n'); return 0; } // cLay varsion 20200509-1 // --- original code --- // int N, K, A[1000], B[1000]; // graph g; // Modint res; // // int up[1000], d[1000]; // int vis[1000][1000]; // Modint dp[1000][1000]; // Modint solve(int n, int k){ // Modint res = 1; // if(k<0) return 0; // if(vis[n][k]) return dp[n][k]; // vis[n][k] = 1; // rep[g.edge[n]](i,g.es[n]){ // if(i==up[n]) continue; // res *= solve(i,k); // } // res += solve(n,k-1); // return dp[n][k] = res; // } // // Modint dp2[1000][1000]; // void dfs(int n){ // if(up[n]==-1){ // dp2[n][0] = 1; // res += dp[n][K-1]; // } else { // Modint s = 0, t; // rep(i,K){ // t = dp[up[n]][i] - if[i, dp[up[n]][i-1], 0]; // t /= dp[n][i]; // s += dp2[up[n]][i]; // dp2[n][i] = t * s; // } // s = 0; // rep(i,1,K){ // s += dp2[n][i-1]; // res += (dp[n][i]-dp[n][i-1]) * s; // } // } // // // wt("---",n,res); // // wt(dp[n](K)); // // wt(dp2[n](K)); // // rep[g.edge[n]](i,g.es[n]){ // if(i==up[n]) continue; // dfs(i); // } // } // // { // rd(N,K,(A--,B--)(N-1)); // g.setEdge(N,N-1,A,B); // // g.getDist(0, d); // up[0] = -1; // rep(i,N) rep[g.edge[i]](j,g.es[i]) if(d[j]==d[i]-1) up[i] = j; // // solve(0, K-1); // dfs(0); // // wt(res); // }