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
M=10**9+7
N=10**5*2
fac=[0]*(N+1)
fac[0]=b=1
for i in range(1,N+1):fac[i]=b=b*i%M
inv=[0]*(N+1)
inv[N]=b=pow(fac[N],M-2,M)
for i in range(N,0,-1):inv[i-1]=b=b*i%M
n,*t=open(0).read().split()
n=int(n)
e=[[]for _ in range(n)]
for a,b in zip(*[map(int,t)]*2):
    e[a-1]+=b-1,
    e[b-1]+=a-1,
o=[]
s=[0]
f=[1]*n
while s:
    v=s.pop()
    f[v]=0
    o+=v,
    l=[]
    for w in e[v]:
        if f[w]:
            l+=w,
            s+=w,
    e[v]=l
sz1,sz2=[0]*n,[0]*n
dp1,dp2=[0]*n,[0]*n
c=[[]for _ in range(n)]
for v in o[::-1]:
    s=1
    c1,c2=[1],[1]
    for w in e[v]:
        u=sz1[w]
        c1+=c1[-1]*dp1[w]*inv[u]%M,
        s+=u
    for w in e[v][::-1]:
        c2+=c2[-1]*dp1[w]*inv[sz1[w]]%M,
    c[v]=c1,c2[::-1]
    sz1[v]=s
    dp1[v]=c1[-1]*fac[s-1]%M
# print(dp1)
sz2[0]=1
dp2[0]=1
for v in o:
    l=len(e[v])
    c1,c2=c[v]
    uv=sz2[v]-1
    tv=dp2[v]*inv[uv]
    for i,w in enumerate(e[v]):
        tw=c1[i]*c2[i+1]%M
        uw=uv+sz1[v]-sz1[w]-1
        dp2[w]=tv*tw*fac[uw]%M
        sz2[w]=uw+2
# print(dp2)
a=[]
for dp1,dp2,sz1,sz2 in zip(dp1,dp2,sz1,sz2):
    sz1-=1
    sz2-=1
    a+=str(dp1*dp2*inv[sz1]*inv[sz2]*fac[sz1+sz2]%M),
print('\n'.join(a))