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
# include <iostream>
# include <algorithm>
# include <cstring>
using namespace std;

struct Edge{
    int next,to;
}E[500000];
int head[200010],cnt=0;
void add(int x,int y)
{
    E[++cnt].to = y;
    E[cnt].next = head[x];
    head[x] = cnt;
}
const long long mod = 1e9+7;
long long siz[200010];
long long N;
long long inv(long long x)
{
    long long ans = 1;
    long long tmp = x;
    long long TT = mod-2;
    while(TT)
    {
        if (TT&1) ans=ans*tmp%mod;
        tmp = tmp*tmp%mod;
        TT>>=1;
    }
    return ans;
}

void dfs1(int x,int f)
{
    siz[x] = 1;
    for (int i=head[x];i;i=E[i].next)
    {
        int to = E[i].to;
        if (to==f) continue;
        dfs1(to,x);
        siz[x]+=siz[to];
    }
}
long long dp[2000000];
void dfs(int x,int f)
{
    if (x!=1)
    {
        dp[x] = dp[f]*siz[x]%mod*inv(N-siz[x])%mod;
    }
    for (int i=head[x];i;i=E[i].next)
    {
        int to = E[i].to;
        if (to==f) continue;
        dfs(to,x);
    }
}
int main(void)
{
    // freopen("aaa.in","r",stdin);
    scanf("%lld",&N);
    for (int i=1,x,y;i<N;i++)
    {
        scanf("%d%d",&x,&y);
        add(x,y);
        add(y,x);
    }
    dfs1(1,0);
    long long tmp = 1;
    for (int i=1;i<=N;i++)
    {
        tmp = tmp*siz[i]%mod;
    }
    long long nn = 1;
    for (long long i=1;i<=N;i++) nn = nn*i%mod;
    // cout<<nn<<endl;
    // cout<<tmp<<endl;
    dp[1] = nn*inv(tmp)%mod;
    dfs(1,0);
    for (int i=1;i<=N;i++)
    printf("%lld\n",dp[i]);
    return 0;
}