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 <vector>
#include <string>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <fstream>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int mod = 1000000007;

vector<int> g[200005];
int n, d[200005];
ll f[200005] = {1}, e[200005], h[200005], z[200005], w[200005], b[200005], c[200005];

ll inv(ll a) {
    ll b = mod - 2, c = 1;
    while (b) {
        if (b % 2) c = c * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return c;
}

void dfs(int x, int p) {
    d[x] = z[x] = h[x] = b[x] = c[x] = 1;
    for (int i : g[x]) if (i != p) {
        dfs(i, x);
        d[x] += d[i];
        z[x] = z[x] * z[i] % mod * e[d[i]] % mod;
        c[x] = c[x] * e[d[i]] % mod;
        b[x] = b[x] * z[i] % mod;
    }
    z[x] = z[x] * f[d[x] - 1] % mod;
}

void dfs2(int x, int p) {
    for (int i : g[x]) if (i != p) {
        h[i] = c[x] * f[d[i]] % mod * f[n - d[i] - 1] % mod * e[n - d[x]] % mod * b[x] % mod * inv(z[i]) % mod * h[x] % mod;
        dfs2(i, x);
    }
    w[x] = f[n - 1] * c[x] % mod * e[n - d[x]] % mod * b[x] % mod * h[x] % mod;
}

int main() {
    ios::sync_with_stdio(false);
    int u, v;
    e[200000] = 750007460;
    h[1] = 1;
    for (int i = 1; i <= 200000; i++) f[i] = f[i - 1] * i % mod;
    for (int i = 199999; i >= 0; i--) e[i] = e[i + 1] * (i + 1) % mod;
    cin >> n;
    for (int i = 1; i < n; i++) cin >> u >> v, g[u].push_back(v), g[v].push_back(u);
    dfs(1, 1);
    dfs2(1, 1);
    for (int i = 1; i <= n; i++) cout << w[i] << '\n';
}
