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

见题面

见题面