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
def main():
    mod = 10**9+7
    fact = [1, 1]
    for i in range(2, 200000):
        fact.append(fact[-1]*i % mod)
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]
    g2 = [set(i) for i in g]
    child = [1]*n  # 子の数
    q = [-1, 0]
    while len(q) > 1:  # DFS
        i = q[-1]
        if g2[i]:
            j = g2[i].pop()
            g2[j].remove(i)
            q.append(j)
        else:
            q.pop()
            if len(q) > 1:
                child[q[-1]] += child[i]
    rank = [(j, i) for i, j in enumerate(child)]
    rank = [j for i, j in sorted(rank)]
    dp = [1]*n
    for i in rank:
        c = child[i]
        ans = fact[c-1]
        temp = 1
        for j in g[i]:
            if child[j] < c:
                ans = ans*dp[j] % mod
                temp = temp*fact[child[j]] % mod
        dp[i] = ans*pow(temp, mod-2, mod) % mod
    dp2 = [0]*n
    dp2[0] = dp[0]
    g2 = [set(i) for i in g]
    q = [-1, 0]
    while len(q) > 1:  # DFS
        i = q[-1]
        if g2[i]:
            j = g2[i].pop()
            c = child[j]
            temp = fact[n-c]*fact[c-1]
            dp2[j] = dp2[i]*(fact[c]*fact[n-c-1])*pow(temp, mod-2, mod) % mod
            g2[j].remove(i)
            q.append(j)
        else:
            q.pop()
            if len(q) > 1:
                child[q[-1]] += child[i]

    for i in dp2:
        print(i)


main()