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
from functools import *
from itertools import *
import sys
sys.setrecursionlimit(10**6)
input = sys.stdin.buffer.readline
 
M = 10**9+7
N = int(input())

@lru_cache(maxsize=None)
def mod_inv(x):
  return 1 if x == 1 else M // x * -mod_inv(M%x) % M

Weight = [0]*(N+1)
Size = [0]*(N+1)
def calc_subtree(v):
  W, S = 1, 1
  for child in Edge[v]:
    Edge[child].remove(v)
    calc_subtree(child)
    W = W * Weight[child] % M
    S += Size[child]
  Weight[v] = W * S % M
  Size[v] = S

Ans = [0]*(N+1)
def calc_ans(v, a):
  Ans[v] = a
  for child in Edge[v]:
    n = Size[child]
    calc_ans(child, a * n * mod_inv(N-n) % M)

Edge = [set() for i in range(N+1)]
fact = N
for i in range(1, N):
  fact = fact * i % M
  a, b = map(int, input().split())
  Edge[a].add(b)
  Edge[b].add(a)
  
calc_subtree(1)
calc_ans(1, mod_inv(Weight[1]) * fact % M)

for a in islice(Ans, 1, None):
  print(a)

