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 = 10 ** 9 + 7
inv = [None, 1]
for i in range(2, 10 ** 5 * 2 + 1):
    inv.append(MOD - MOD // i * inv[MOD % i] % MOD)

fact = [1]
ifact = [1]
for i in range(1, 10 ** 5 * 2 + 1):
    fact.append((i * fact[-1]) % MOD)
    ifact.append((inv[i] * ifact[-1]) % MOD)


class Node:
    def __init__(self, ind):
        self.ind = ind
        self.val = 1
        self.ndesc = 1
        self.neighs = []


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

stack = [(-1, nodes[0])]
for i in range(N):
    fro, node = stack[i]
    for neigh in node.neighs:
        if neigh.ind == fro:
            continue
        stack.append((node.ind, neigh))

for i in range(N - 1, -1, -1):
    fro, node = stack[i]
    node.val = node.val * fact[node.ndesc - 1] % MOD
    if fro == -1:
        continue
    nodes[fro].ndesc += node.ndesc
    nodes[fro].val = nodes[fro].val * node.val * ifact[node.ndesc] % MOD

stack = [(-1, node, nodes[0].val * inv[N] % MOD)]
for i in range(N):
    fro, node, val = stack[i]
    node.val = val * node.ndesc * inv[max(1, N - node.ndesc)] % MOD
    for neigh in node.neighs:
        if neigh.ind == fro:
            continue
        stack.append((node.ind, neigh, node.val))

for i in range(N):
    print(nodes[i].val)
