Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2
1 3

Sample Output 1

2
1
1

The graph in this input is as follows:

For k=1, there are two ways in which we can write the numbers on the vertices, as follows:

Writing 1, 2, 3 on Vertex 1, 2, 3, respectively

Writing 1, 3, 2 on Vertex 1, 2, 3, respectively

Sample Input 2

2
1 2

Sample Output 2

1
1

The graph in this input is as follows:

Sample Input 3

5
1 2
2 3
3 4
3 5

Sample Output 3

2
8
12
3
3

The graph in this input is as follows:

Sample Input 4

8
1 2
2 3
3 4
3 5
3 6
6 7
6 8

Sample Output 4

40
280
840
120
120
504
72
72

The graph in this input is as follows:

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

#define MOD 1000000007
#define MOD2 998244353
#define int long long
#define double long double
#define EPS 1e-9
//#define PI 3.14159265358979

#define rep(i, n) for (int i = 0; i < (int)(n); i++)

using namespace std;

template < typename T >
ostream &operator<<(ostream &os, const vector< T > &A) {
	for (int i = 0; i < A.size(); i++)
		os << A[i] << " ";
	os << endl;
	return os;
}
template <>
ostream &operator<<(ostream &os, const vector< vector< int > > &A) {
	int N = A.size();
	int M;
	if (N > 0)
		M = A[0].size();
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++)
			os << A[i][j] << " ";
		os << endl;
	}
	return os;
}

typedef pair< int, int > pii;
typedef long long ll;

struct edge {
	int from, to, d, c;
	edge(int _from = 0, int _to = 0, int _d = 0, int _c = 0) {
		from = _from;
		to = _to;
		d = _d;
		c = _c;
	}
	bool operator<(const edge &rhs) const {
		return (d == rhs.d) ? (c < rhs.c) : (d < rhs.d);
	}
};
struct aabb {
	int x1, y1, x2, y2;
	aabb(int x1, int y1, int x2, int y2) : x1(x1), y1(y1), x2(x2), y2(y2) {}
};

typedef vector< edge > edges;
typedef vector< edges > graph;
struct flow {
	int to, cap, rev, cost;
	flow(int to = 0, int cap = 0, int rev = 0, int cost = 0) : to(to), cap(cap), rev(rev), cost(cost) {}
};
typedef vector< vector< flow > > flows;

const int di[4] = {0, -1, 0, 1};
const int dj[4] = {-1, 0, 1, 0};
const int ci[5] = {0, 0, -1, 0, 1};
const int cj[5] = {0, -1, 0, 1, 0};
const ll LINF = LLONG_MAX / 2;
const int INF = INT_MAX / 2;
const double PI = acos(-1);

int pow2(int n) { return 1LL << n; }
template < typename T, typename U >
bool chmin(T &x, const U &y) {
	if (x > y) {
		x = y;
		return true;
	}
	return false;
}
template < typename T, typename U >
bool chmax(T &x, const U &y) {
	if (x < y) {
		x = y;
		return true;
	}
	return false;
}

struct initializer {
	initializer() {
		cout << fixed << setprecision(20);
	}
};
initializer _____;
ll gcd(ll a, ll b) {
	if (b == 0)
		return a;
	else
		return gcd(b, a % b);
}
ll extgcd(ll a, ll b, ll &x, ll &y) {
	int d = a;
	if (b != 0) {
		d = extgcd(b, a % b, y, x);
		y -= (a / b) * x;
	} else {
		x = 1;
		y = 0;
	}
	return d;
}
ll factorial(ll x) {
	if (x == 1)
		return 1;
	else
		return x * factorial(x - 1);
}
ll Mfactorial(ll x, ll m) {
	ll ret = 1;
	for (ll i = 1; i <= x; i++) {
		ret *= i;
		ret %= m;
	}
	return ret;
}
vector< int > MfactTable(int n, int m) {
	vector< int > ret(n + 1);
	ret[0] = 1;
	int tmp = 1;
	for (int i = 1; i <= n; i++) {
		tmp *= i;
		tmp %= m;
		ret[i] = tmp;
	}
	return ret;
}
int Minverse(int a, int m) {
	int x, y;
	extgcd(a, m, x, y);
	return (m + x % m) % m;
}
int McombSmall(int n, int k, int m) {
	//O(n)
	if (k > n)
		return 0;
	int ret = Mfactorial(n, m);
	ret *= Minverse(Mfactorial(k, m), m);
	ret %= m;
	ret *= Minverse(Mfactorial(n - k, m), m);
	return ret % m;
}
int McombFromFactTable(vector< int > &T, int n, int k, int m) {
	if (k > n)
		return 0;
	int ret = T[n];
	ret *= Minverse(T[k], m);
	ret %= m;
	ret *= Minverse(T[n - k], m);
	return ret % m;
}
ll pow(ll x, int n) {
	if (n == 0)
		return 1;
	ll ret = (n & 1) ? x : 1;
	ll a = pow(x, n / 2);
	return ret * a * a;
}
ll Mpow(ll x, int n, int m) {
	if (n == 0)
		return 1;
	ll ret = (n & 1) ? x : 1;
	ll a = Mpow(x, n / 2, m);
	return (((ret * a) % m) * a) % m;
}
vector< vector< int > > combTable(int N) {
	vector< vector< int > > ret(N + 1, vector< int >(N + 1));
	for (int i = 0; i <= N; i++)
		for (int j = 0; j <= i; j++) {
			if (j == 0 || j == i)
				ret[i][j] = 1;
			else
				ret[i][j] = ret[i - 1][j - 1] + ret[i - 1][j];
		}
	return ret;
}
int countNmodPisQlr(int l, int r, int P, int Q) {
	//r>=l>=0
	return (r - Q + P) / P - (l - Q + P - 1) / P;
}
struct Combination {
	int N = 0, M;
	vector< int > Ftable, FItable, Inversetable;
	void init() {
		Ftable.resize(N + 1);
		FItable.resize(N + 1);
		Inversetable.resize(N + 1);
		Ftable[0] = 1;
		FItable[0] = 1;
		for (int i = 1; i <= N; i++)
			Ftable[i] = Ftable[i - 1] * i % M;
		FItable[N] = Minverse(Ftable[N], M);
		for (int i = N - 1; i >= 1; i--)
			FItable[i] = FItable[i + 1] * (i + 1) % M;
		Inversetable[1] = 1;
		for (int i = 2; i <= N; i++)
			Inversetable[i] = M - Inversetable[M % i] * (M / i) % M;
	}
	Combination(int max, int mod) {
		N = max;
		M = mod;
		init();
	}
	Combination() {}
	int calc(int n, int k) {
		if (k > n)
			return 0;
		int ret = Ftable[n] * FItable[k] % M * FItable[n - k] % M;
		return ret;
	}
	int inverse(int n) { return Inversetable[n]; }
	int factorial(int n) { return Ftable[n]; }
	int factorialInverse(int n) { return FItable[n]; }
};
int N, M, K, T, Q, H, W;
vector< vector< pii > > dp;
Combination cmb;
pii dfs(graph &G, int x, int y, int p) {
	if (dp[x][y] != pii(-1, -1))
		return dp[x][y];
	int n = 0;
	vector< pii > A;
	for (auto e : G[x]) {
		if (e.to == p)
			continue;
		pii ret = dfs(G, e.to, e.d, x);
		n += ret.second;
		A.push_back(ret);
	}
	pii ret(1, 0);
	ret.second = n + 1;
	rep(i, A.size()) {
		ret.first *= A[i].first * cmb.calc(n, A[i].second) % MOD;
		ret.first %= MOD;
		n -= A[i].second;
	}
	return dp[x][y] = ret;
}
signed main() {
	cin >> N;
	graph G(N);
	cmb = Combination(N + 10, MOD);
	dp.assign(N, vector< pii >(N, pii(-1, -1)));
	rep(i, N - 1) {
		int a, b;
		cin >> a >> b;
		--a;
		--b;
		G[a].emplace_back(a, b, i);
		G[b].emplace_back(b, a, i);
	}
	rep(k, N) {
		pii ans = dfs(G, k, N - 1, -1);
		cout << ans.first << endl;
	}
	return 0;
}