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

nn = 200200
mod = 10**9+7

fa = [1] * (nn+1)
fainv = [1] * (nn+1)
inv = [1] * (nn+1)
for i in range(nn):
    fa[i+1] = fa[i] * (i+1) % mod
fainv[-1] = pow(fa[-1], mod-2, mod)
for i in range(nn)[::-1]:
    fainv[i] = fainv[i+1] * (i+1) % mod
for i in range(1, nn)[::-1]:
    inv[i] = fainv[i] * fa[i-1]

C = lambda a, b: fa[a] * fainv[b] % mod * fainv[a-b] % mod if 0 <= b <= a else 0

N = int(input())
X = [[] for i in range(N)]
for i in range(N-1):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)

P = [-1] * N
Q = deque([0])
R = []
while Q:
    i = deque.popleft(Q)
    R.append(i)
    for a in X[i]:
        if a != P[i]:
            P[a] = i
            X[a].remove(i)
            deque.append(Q, a)

BU = [1] * N
TD = [1] * N
SI = [1] * N
for i in R[::-1]:
    a = 1
    s = 1
    for j in X[i]:
        a = a * BU[j] % mod
        s += SI[j]
    SI[i] = s
    BU[i] = inv[s] * a % mod

for i in R:
    c = len(X[i])
    AR = [1] * (c + 1)
    AL = 1
    for k in range(c-1, 0, -1):
        j = X[i][k]
        AR[k] = AR[k+1] * BU[j] % mod
    for k, j in enumerate(X[i]):
        TD[j] = TD[i] * AL % mod * AR[k+1] % mod * inv[N - SI[j]] % mod
        AL = AL * BU[j] % mod

for i in range(N):
    print(BU[i] * fa[SI[i]] % mod * TD[i] % mod * fa[N - SI[i]] % mod * C(N-1, SI[i] - 1) % mod)