#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) void*wmem; char memarr[96000000]; template inline S max_L(S a,T b){ return a>=b?a:b; } 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 setEdgeRootedTree(int N__, int M, int A[], int B[], int root=0, int reorder=0, int cnv[] = NULL, void **mem = &wmem){ int i; int j; int k; int*dist; int*q; int qs; int qe; int*ind; void*tmem; N = N__; tmem = ((char*)(*mem)) + (sizeof(int) * N + 15) + (sizeof(int*) * N + 15) + (sizeof(int) * M + 15 * 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], &tmem); } 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]; } walloc1d(&dist, N, &tmem); walloc1d(&q, N, &tmem); walloc1d(&ind, N, &tmem); if(cnv==NULL){ walloc1d(&cnv, N, &tmem); } for(i=(0);i<(N);i++){ dist[i] = -1; } dist[root] = 0; qs = qe = 0; q[qe++] = root; while(qs < qe){ i = q[qs++]; for(j=(0);j<(es[i]);j++){ k = edge[i][j]; if(dist[k]==-1){ dist[k] = dist[i] + 1; q[qe++] = k; } } } if(reorder == 0){ for(i=(0);i<(N);i++){ cnv[i] = i; } for(i=(0);i<(N);i++){ ind[i] = i; } } else{ for(i=(0);i<(N);i++){ cnv[i] = q[i]; } for(i=(0);i<(N);i++){ ind[cnv[i]] = i; } } for(i=(0);i<(N);i++){ es[i] = 0; } for(i=(0);i<(M);i++){ j = A[i]; k = B[i]; if(dist[j] > dist[k]){ swap(j, k); } es[ind[j]]++; } 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++){ j = A[i]; k = B[i]; if(dist[j] > dist[k]){ swap(j, k); } j = ind[j]; k = ind[k]; edge[j][es[j]++] = k; } } 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 A[1000]; int B[1000]; int C; graph g; int dist[1001]; int dmax[1001]; Modint memo[1001]; Modint dp[1000][1001]; int main(){ int i, r; wmem = memarr; Modint res = 0; Modint tmp; rd(N); rd(C); { int Lj4PdHRW; for(Lj4PdHRW=(0);Lj4PdHRW<(N-1);Lj4PdHRW++){ rd(A[Lj4PdHRW]);A[Lj4PdHRW] += (-1); rd(B[Lj4PdHRW]);B[Lj4PdHRW] += (-1); } } g.setEdge(N,N-1,A,B); for(i=(0);i<(N);i++){ g.getDist(i,dist); { int RZTsC2BF; int FmcKpFmN; if(N==0){ FmcKpFmN = 0; } else{ FmcKpFmN = dist[0]; for(RZTsC2BF=(1);RZTsC2BF<(N);RZTsC2BF++){ FmcKpFmN = max_L(FmcKpFmN, dist[RZTsC2BF]); } } dmax[i] =FmcKpFmN; } } { int KrdatlYV; int ao_dF3pO = 0; int tU__gIr_; int a2conNHc; int hCmBdyQB; for(KrdatlYV=(0);KrdatlYV<(((N)-1)+1);KrdatlYV++){ a2conNHc = dmax[KrdatlYV]; if(ao_dF3pO==0 || tU__gIr_>a2conNHc){ tU__gIr_ = a2conNHc; ao_dF3pO = 1; hCmBdyQB = KrdatlYV; } } g.setEdgeRootedTree(N,N-1,A,B,hCmBdyQB,1); } for(r=(2);r<(N+1);r++){ int j, k; for(i=(N)-1;i>=(0);i--){ int j; for(j=(0);j<(r);j++){ int XJIcIBrW; tmp = 1; for(XJIcIBrW=(0);XJIcIBrW<(g.es[i]);XJIcIBrW++){ auto &k = g.edge[i][XJIcIBrW]; if(j-1 >= 0){ if(j+1 < r){ tmp *=dp[k][j-1]+dp[k][j+1]; } else{ tmp *=dp[k][j-1]+0; } } else{ if(j+1 < r){ tmp *=0+dp[k][j+1]; } else{ tmp *=0+0; } } } dp[i][j] = tmp; } } for(j=(0);j<(r);j++){ memo[r] += dp[0][j]; } for(j=(1);j<(r);j++){ memo[r] -= memo[j] * (r-j+1); } if(memo[r]==0){ break; } for(k=(0);k<(3);k++){ i = (C + k) / 3; if(i >= r){ res += memo[r] * (i-r+1); } } } wt_L(res); wt_L('\n'); return 0; } // cLay varsion 20200911-1 // --- original code --- // int N, A[1000], B[1000], C; // graph g; // // int dist[1001], dmax[1001]; // Modint memo[1001]; // Modint dp[1000][1001]; // // { // // Modint res = 0, tmp; // rd(N,C,(A--,B--)(N-1)); // // g.setEdge(N,N-1,A,B); // rep(i,N) g.getDist(i,dist), dmax[i] = max(dist(N)); // g.setEdgeRootedTree(N,N-1,A,B,argmin(dmax(N)),1); // // rep(r,2,N+1){ // rrep(i,N) rep(j,r){ // tmp = 1; // rep[g.edge[i]](k,g.es[i]){ // // wt("edge",i,k); // tmp *= if[j-1 >= 0, dp[k][j-1], 0] + if[j+1 < r, dp[k][j+1], 0]; // } // dp[i][j] = tmp; // // wt(r,i,j,tmp); // } // rep(j,r) memo[r] += dp[0][j]; // rep(j,1,r) memo[r] -= memo[j] * (r-j+1); // if(memo[r]==0) break; // // wt("r",r,memo[r]); // // rep(k,3){ // i = (C + k) / 3; // if(i >= r) res += memo[r] * (i-r+1); // } // } // // wt(res); // }