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)
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

inv = lambda i: fainv[i] * fa[i-1] % mod

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)

unit = 1
f = lambda a, b: a * b % mod
g_bu = lambda a, i=-1: a * inv(SI[i]) % mod
g_td = lambda a, i=-1: a * inv(N - SI[i]) % mod

SI = [1] * N
for i in R[1:][::-1]:
    SI[P[i]] += SI[i]

BU = [unit] * N
TD = [unit] * N
for i in R[1:][::-1]:
    BU[i] = g_bu(BU[i], i)
    p = P[i]
    BU[p] = f(BU[p], BU[i])
BU[R[0]] = g_bu(BU[R[0]], R[0])

AX = [1] * N
for i in R:
    ac = unit
    for j in X[i]:
        AX[j] = ac
        ac = f(ac, BU[j])
    ac = unit
    for j in X[i][::-1]:
        AX[j] = f(AX[j], ac)
        TD[j] = g_td(f(TD[i], AX[j]), j)
        ac = f(ac, BU[j])

print(*[BU[i] * SI[i] % mod * TD[i] % mod * fa[N - 1] % mod for i in range(N)], sep = "\n")