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 <cstdio>
#include <vector>
#include <map>
#include <algorithm>

const int MAX_N = 2e5 + 5;
const int MOD = 1e9 + 7;

long long pow(long long base, int exp)
{
	long long res = 1;
	for (; exp; exp >>= 1)
	{
		if (exp & 1)
			res = res * base % MOD;
		base = base * base % MOD;
	}
	return res;
}

int n, cnt[MAX_N], par[MAX_N];
long long val[MAX_N], fwd[MAX_N], bwd[MAX_N], ans[MAX_N];
std::vector<int> adj[MAX_N];

long long binom(int n, int k)
{
	return fwd[n] * bwd[k] % MOD * bwd[n - k] % MOD;
}

void init(int x, int p)
{
	par[x] = p;
	val[x] = 1;
	for (int y : adj[x])
		if (y != p)
		{
			init(y, x);
			val[x] = val[x] * val[y] % MOD * binom(cnt[x] + cnt[y] + 1, cnt[x]) % MOD;
			cnt[x] += cnt[y] + 1;
		}
}

std::map<int, long long> map[MAX_N];

void solve(int x, int p)
{
	if (x == 1) ans[x] = val[x];
	else ans[x] = val[x] * map[p][x] % MOD * binom(n - 1, cnt[x]) % MOD;
	for (int y : adj[x])
		if (y != p)
		{
			map[x][y] = ans[x] * pow(val[y], MOD - 2) % MOD * pow(binom(n - 1, cnt[y] + 1), MOD - 2) % MOD;
			solve(y, x);
		}
}

int main()
{
	fwd[0] = bwd[0] = 1;
	for (int i = 1; i < MAX_N; ++i)
	{
		fwd[i] = fwd[i - 1] * i % MOD;
		bwd[i] = pow(fwd[i], MOD - 2);
	}
	scanf("%d", &n);
	for (int i = 1; i < n; ++i)
	{
		int u, v; scanf("%d%d", &u, &v);
		adj[u].push_back(v);
		adj[v].push_back(u);
	}
	init(1, 0);
	solve(1, 0);
	for (int i = 1; i <= n; ++i)
		printf("%lld\n", ans[i]);
}