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
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
def main():
    n=int(input())
    def cmb(n, r, mod):
        if ( r<0 or r>n ):
            return 0
        r = min(r, n-r)
        return g1[n] * g2[r] * g2[n-r] % mod
    mod = 10**9+7 #出力の制限
    g1 = [1, 1] # 元テーブル
    g2 = [1, 1] #逆元テーブル
    inverse = [0, 1] #逆元テーブル計算用テーブル
    for i in range( 2, n + 1 ):
        g1.append( ( g1[-1] * i ) % mod )
        inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
        g2.append( (g2[-1] * inverse[-1]) % mod )

    ki=[[] for _ in range(n)]
    for _ in range(n-1):
        a,b=map(int,input().split())
        a,b=a-1,b-1
        ki[a].append(b)
        ki[b].append(a)
    memo={} # memo[(p,v)]:p->vの部分木のサイズ、整数の書き方
    def dfs(p,v):
        if (p,v) in memo:return memo[(p,v)]
        size,pat=0,1
        tmps,tmpp=1,1
        deg=len(ki[v])
        for nv in ki[v]:
            if nv==p:continue
            si,pi=dfs(v,nv)
            size+=si
            tmps*=g2[si]
            tmps%=mod
            tmpp*=pi
            tmpp%=mod
        pat=(g1[size]*tmps*tmpp)%mod
        memo[(p,v)]=(size+1,pat)
        return (size+1,pat)
    ans=[0]*n
    def bfs(p,v,res):
        if p!=-1:memo[(v,p)]=res
        deg=len(ki[v])
        tmps,tmpp=1,1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmps*=g2[si]
            tmpp*=pi
            tmps%=mod
            tmpp%=mod

        ans[v]=g1[n-1]*tmps*tmpp
        ans[v]%=mod

        dpl=[1]*(deg+1)
        dpr=[1]*(deg+1)
        tmp=1
        for i in range(deg):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpl[i+1]=tmp
        tmp=1
        for i in range(deg-1,-1,-1):
            si,pi=memo[(v,ki[v][i])]
            tmp*=pi*g2[si]
            tmp%=mod
            dpr[i]=tmp
        for i in range(deg):
            nv=ki[v][i]
            if p==nv:continue
            bfs(v,nv,(n-memo[(v,nv)][0],(g1[n-1-memo[(v,nv)][0]]*dpl[i]*dpr[i+1])%mod))
    dfs(-1,0)
    #print(memo)
    bfs(-1,0,0)
    print(*ans,sep='\n')
    #print(memo)

if __name__=='__main__':
    main()
