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
n=int(input())
F = n+5
mod = 10**9+7
fact = [1]*F
inv = [1]*F
for i in range(2,F):
    fact[i]=(fact[i-1]*i)%mod
inv[F-1]=pow(fact[F-1],mod-2,mod)
for i in range(F-2,1,-1):
    inv[i] = (inv[i+1]*(i+1))%mod

#invnum[0] cant be used
invnum=[fact[i-1]*inv[i] for i in range(n)]

graph=[[] for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    graph[a-1].append(b-1)
    graph[b-1].append(a-1)

stack=[0]
order=[0]
parent=[-1]*n
comb=[0]*n
size=[1]*n

# BFS order
while stack:
    node = stack.pop()
    for neib in graph[node]:
        if neib!=parent[node]:
            stack.append(neib)
            order.append(neib)
            parent[neib]=node

#calc size including self
for node in order[n-1:0:-1]:
    size[parent[node]]+=size[node]

#calc root comb
comb[0]=fact[n-1]
for node in range(1,n):
    comb[0]*=invnum[size[node]]
    comb[0]%=mod

#calc all comb
for node in order[1:]:
    comb[node]=comb[parent[node]]*size[node]*invnum[n-size[node]]%mod

print(*comb,sep="\n")