Problem Statement

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.