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
import sys
input=sys.stdin.readline
from collections import deque

def main():
    mod=1000000007
    inv=lambda x: pow(x,mod-2,mod)    
    n=int(input())
    Fact=[1]
    for i in range(1,n+1):
        Fact.append(Fact[i-1]*i%mod)
    Finv=[0]*(n+1)
    Finv[-1]=inv(Fact[-1])
    for i in range(n-1,-1,-1):
        Finv[i]=Finv[i+1]*(i+1)%mod
    Edges=[[] for _ in range(n)]
    for _ in range(n-1):
        a,b=map(int,input().split())
        a-=1; b-=1
        Edges[a].append(b)
        Edges[b].append(a)
    Stack=[0]
    Par=[-1]*n
    Order=[]
    while Stack:
        v=Stack.pop()
        Order.append(v)
        for c in Edges[v]:
            if c!=Par[v]:
                Stack.append(c)
                Par[c]=v
    DP=[1]*n
    Size=[1]*n
    for v in Order[::-1]:
        DP[v]*=Fact[Size[v]-1]
        DP[v]%=mod
        p=Par[v]
        if p==-1:
            continue
        Size[p]+=Size[v]
        DP[p]*=DP[v]*Finv[Size[v]]
        DP[p]%=mod
    Ans=[0]*n
    que=deque()
    que.append((0,-1,1))
    while que:
        v,par,par_cnt=que.popleft()
        Left=[1]
        for to in Edges[v]:
            tmp=DP[to]*Finv[Size[to]]
            if to==par:
                tmp=par_cnt*Finv[n-Size[v]]
            Left.append(Left[-1]*tmp%mod)
        Right=[1]
        for to in reversed(Edges[v]):
            tmp=DP[to]*Finv[Size[to]]
            if to==par:
                tmp=par_cnt*Finv[n-Size[v]]
            Right.append(Right[-1]*tmp%mod)
        Ans[v]=Left[-1]*Fact[n-1]%mod
        m=len(Edges[v])
        for i,to in enumerate(Edges[v]):
            if to!=par:
                que.append((to,v,Left[i]*Right[m-i-1]*Fact[n-Size[to]-1]%mod))
    print(*Ans,sep="\n")
    
if __name__=='__main__':
    main()