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

MOD = 10 ** 9 + 7

class Factorial:
    def __init__(self, n, mod):
        self.f = [1]
        self.mod = mod
        for j in range(1, n + 1):
            self.f.append(self.f[-1] * j % mod)
        self.i = [pow(self.f[-1], mod - 2, mod)]
        for j in range(n, 0, -1):
            self.i.append(self.i[-1] * j % mod)
        self.i.reverse()
    def factorial(self, j):
        return self.f[j]
    def ifactorial(self, j):
        return self.i[j]
    def comb(self, n, k):
        return self.f[n] * self.i[n - k] % self.mod * self.i[k] % self.mod if n >= k else 0

N = int(input())


C = Factorial(N + 1, MOD)

G = [[] for _ in range(N)]
for _ in range(N - 1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    G[a].append(b)
    G[b].append(a)

order = []
order_append = order.append

stack = [(0, -1)]
stack_pop = stack.pop
stack_append = stack.append

while stack:
    tmp = stack_pop()
    order_append(tmp)
    for next_ in G[tmp[0]]:
        if next_ == tmp[1]:
            continue
        stack_append((next_, tmp[0]))
    
size = [1] * N
dp = [1] * N

# print (order)
for c, p in order[::-1]:
    if c == 0:
        break
    size[p] += size[c]

for c, p in order[::-1]:
    dp[c] = (dp[c] * C.factorial(size[c] - 1)) % MOD
    if c == 0:
        break
    # dp[c] = (dp[c] * C.factorial(size[c] - 1)) % MOD
    dp[p] = (dp[p] * dp[c] % MOD) * C.ifactorial(size[c]) % MOD

# print (dp)
dp2 = [0] * N
dp2[0] = dp[0]

for c, p in order[1::]:
    tmp = (dp2[p] * C.factorial(N - 1 - size[c]) % MOD) * C.factorial(size[c]) % MOD
    red = (tmp * C.ifactorial(N - 1) % MOD) * pow(dp[c], MOD - 2, MOD) % MOD

    size_red = N - size[c]
    tmp = (dp[c] * red % MOD) * C.factorial(N - 1) % MOD
    dp2[c] = (tmp * C.ifactorial(size[c] - 1) % MOD) * C.ifactorial(size_red) % MOD


print (*dp2, sep = '\n')