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
MOD = 1000000007
M = 2*10**5 + 10
fact = [1] * M
ifact = [1] * M
for i in range(2, M):
    fact[i] = fact[i - 1] * i % MOD
ifact[M - 1] = pow(fact[M - 1], MOD - 2, MOD)
for i in range(2, M - 1)[::-1]:
    ifact[i] = ifact[i + 1] * (i + 1) % MOD


def comb(n, k):
    if n < 0 or k > n:
        return 0
    return (fact[n] * ifact[k] % MOD) * ifact[n - k] % MOD


class DP:
    def __init__(self, dp = 1, size = 0):    
        self.dp = dp
        self.size = size

    def __add__(self, other):
        dp = self.dp
        dp *= other.dp
        dp %= MOD
        size = self.size + other.size
        dp *= comb(size, self.size)
        dp %= MOD
        return DP(dp, size)

    def __sub__(self, other):
        size = self.size - other.size
        dp = self.dp
        dp *= pow(comb(self.size, size), MOD - 2, MOD)
        dp %= MOD
        dp *= pow(other.dp, MOD - 2, MOD)
        dp %= MOD
        return DP(dp, size)

    def addRoot(self):
        return DP(self.dp, self.size + 1)


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

order = []
parent = [-1] * N
stack = [0]
while stack:
    v = stack.pop()
    order.append(v)
    for c in e[v]:
        if c == parent[v]:
             continue
        stack.append(c)
        parent[c] = v

dp = [DP() for _ in range(N)]
for v in order[1:][::-1]:
    dp[parent[v]] += dp[v].addRoot()
for v in order[1:]:
    d = dp[parent[v]] - dp[v].addRoot()
    dp[v] += d.addRoot()
for d in dp:
    print(d.dp)