We have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i. For each k=1, ..., N, solve the problem below:

* Consider writing a number on each vertex in the tree in the following manner:
* First, write 1 on Vertex k.
* Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows:
* Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.
* Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq a_i,b_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}


Output

For each k=1, 2, ..., N in this order, print a line containing the answer to the problem.

Examples

Input

3
1 2
1 3


Output

2
1
1


Input

2
1 2


Output

1
1


Input

5
1 2
2 3
3 4
3 5


Output

2
8
12
3
3


Input

8
1 2
2 3
3 4
3 5
3 6
6 7
6 8


Output

40
280
840
120
120
504
72
72
#include<bits/stdc++.h>
#define m 1000000007
#define r(i,n) for(l i=0;i<n;i++)
#define B push_back
using namespace std;
typedef long l;
typedef vector<l> L;
vector<L> p;
l P(l i, l b) {l a=1;r(n,62){if((b>>n)%2){a*=p[i][n];a%=m;}}return a;}
int main(){deque<l>q;l N,X,Y;cin>>N;l M=N-1;L V,A(N,0),a(N,-1),D(N,1),J(N,0),n(N,1),w(70);vector<L>T(N);
	r(i,N*2){w[0]=i;r(j,62)w[j+1]=(w[j]*w[j])%m;p.B(w);}
	r(i,M){cin>>X>>Y;X--;Y--;T[X].B(Y);T[Y].B(X);A[X]++;A[Y]++;	}q.B(0);J[0]=1;V.B(0);
	r(k,N){l x=q.front();q.pop_front();r(i,A[x]){l E=T[x][i];if(!J[E]){J[E]=1;	q.B(E);a[E]=x;V.B(E);}}}
	r(j,N){l i=N-1-j,x=V[i];r(j,A[x]){l E=T[x][j];if(E==a[x])continue;D[x]+=D[E];}}
	r(i,N)n[0]=((n[0]*(i+1)%m)*P(D[i],m-2))%m;
	r(j,N-1){l x=V[j+1];n[x]=(((n[a[x]]*D[x])%m)*P(N-D[x],m-2))%m;}
	r(i,N)cout<<n[i]<<"\n";}