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.buffer.readline
from collections import deque

def main():
	N = int(input())
	edge = [[] for _ in range(N+1)]
	
	MOD = 10**9+7
	fac = [0]*(N+1)
	fac[0],fac[1] = 1,1
	invfac = [0]*(N+1)
	invfac[0],invfac[1] = 1,1

	for i in range(2,N+1):
		fac[i] = (fac[i-1]*i)%MOD

	invfac[-1] = pow(fac[-1],MOD-2,MOD)
	for i in range(N,0,-1):
		invfac[i-1] = (invfac[i]*i)%MOD
	
	for _ in range(N-1):
		a,b = map(int,input().split())
		edge[a].append(b)
		edge[b].append(a)

	proc = []
	parent = [0]*(N+1)
	q = deque([1])
	while q:
		now = q.pop()
		proc.append(now)
		for fol in edge[now]:
			if fol == parent[now]:
				continue
			parent[fol] = now
			q.append(fol)
	
	d_size = [0]*(N+1)
	d_dp = [1]*(N+1)

	for v in proc[::-1]:
		d_dp[v] *= fac[d_size[v]]
		d_dp[v] %= MOD
		p = parent[v]
		s = d_size[v]+1
		d_size[p] += s
		d_dp[p] *= d_dp[v]*invfac[s]
		d_dp[p] %= MOD
	
	u_size = [N-num-1 for num in d_size]
	u_dp = [1]*(N+1)
	
	for v in proc[1:]:
	    p = parent[v]
	    x = d_dp[p]
	    x *= u_dp[p]
	    x *= invfac[d_size[p]]
	    x *= fac[d_size[v]+1]
	    x *= pow(d_dp[v],MOD-2,MOD)
	    x %= MOD
	    x *= fac[u_size[v]-1]
	    x *= invfac[u_size[p]]
	    u_dp[v] = x%MOD
	
	u_size[1] = 0
	u_dp[1] = 1
	
	for i in range(1,N+1):
	    ret = d_dp[i]*u_dp[i]*fac[d_size[i]+u_size[i]]*invfac[d_size[i]]*invfac[u_size[i]]%MOD
	    print(ret)

if __name__ == "__main__":
	main()
