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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using StringBuilder = System.Text.StringBuilder;
using Number = System.Int64;
using System.Numerics;
namespace Program {
	public class Solver {
		public void Solve() {
			var n = sc.Integer();
			var G = Enumerate(n, x => new List<int>());
			for (int i = 0; i < n - 1; i++) {
				var a = sc.Integer() - 1;
				var b = sc.Integer() - 1;
				G[a].Add(b);
				G[b].Add(a);
			}
			var fact = new ModInteger[n + 1];
			var invfact = new ModInteger[n + 1];
			fact[0] = 1;
			for (int i = 1; i <= n; i++)
				fact[i] = fact[i - 1] * i;
			invfact[n] = ModInteger.Pow(fact[n], ModInteger.Mod - 2);
			for (int i = n - 1; i >= 0; i--)
				invfact[i] = invfact[i + 1] * (i + 1);
			DP.Merge = (l, r, f) => {
				var ret = new DP();
				ret.pat = l.pat * r.pat;
				if (f)
					ret.pat *= invfact[r.sz];
				ret.sz = l.sz + r.sz;
				return ret;
			};
			DP.Root = x => {
				var ret = new DP();
				ret.pat = x.pat * fact[x.sz];
				ret.sz = x.sz + 1;
				return ret;
			};

			var dp = new DP[n];
			Func<int, int, DP> dfs = null;
			dfs = (prev, cur) => {
				var ret = new DP();
				foreach (var to in G[cur])
					if (prev != to) ret += dfs(cur, to);
				return dp[cur] = !ret;
			};
			dfs(-1, 0);
			dfs = (prev, cur) => {

				var ret = new DP();
				var k = G[cur].Count;
				var rdp = new DP[k + 1];
				rdp[k] = new DP();
				for (int i = k - 1; i >= 0; i--)
					rdp[i] = rdp[i + 1] + dp[G[cur][i]];
				for (int i = 0; i < k; i++) {
					var to = G[cur][i];
					var pre = dp[to];
					dp[cur] = !(ret + rdp[i + 1]);
					dp[cur].pat *= fact[rdp[i + 1].sz];
					ret += dp[to];
					if (prev != to) dfs(cur, to);
				}
				return dp[cur] = !ret;
			};
			dfs(-1, 0);


			for (int i = 0; i < n; i++)
				Console.WriteLine(dp[i].pat);
		}
		public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
		static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
	static public void Main() {
		var solver = new Program.Solver();
		solver.Solve();
		Program.IO.Printer.Out.Flush();
	}
}
#endregion
#region Ex
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;
	public class Printer : StreamWriter {
		static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
		public static Printer Out { get; set; }
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
		public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
		public void Write<T>(string format, T[] source) { base.Write(format, source.OfType<object>().ToArray()); }
		public void WriteLine<T>(string format, T[] source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
	}
	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }
		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }
		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
			return buf[ptr++];
		}
		public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
				sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n'; b = (char)read())
				if (b == 0) break;
				else if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() {
			if (isEof) return long.MinValue;
			long ret = 0; byte b = 0; var ng = false;
			do b = read();
			while (b != 0 && b != '-' && (b < '0' || '9' < b));
			if (b == 0) return long.MinValue;
			if (b == '-') { ng = true; b = read(); }
			for (; true; b = read()) {
				if (b < '0' || '9' < b)
					return ng ? -ret : ret;
				else ret = ret * 10 + b - '0';
			}
		}
		public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
		public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; }
		private T[] enumerate<T>(int n, Func<T> f) {
			var a = new T[n];
			for (int i = 0; i < n; ++i) a[i] = f();
			return a;
		}

		public char[] Char(int n) { return enumerate(n, Char); }
		public string[] Scan(int n) { return enumerate(n, Scan); }
		public double[] Double(int n) { return enumerate(n, Double); }
		public int[] Integer(int n) { return enumerate(n, Integer); }
		public long[] Long(int n) { return enumerate(n, Long); }
	}
}
#endregion
#region ModNumber
public partial struct ModInteger {
	public const long Mod = (long)1e9 + 7;
	public long num;
	public ModInteger(long n) : this() { num = n % Mod; if (num < 0) num += Mod; }
	public override string ToString() { return num.ToString(); }
	public static ModInteger operator +(ModInteger l, ModInteger r) { var n = l.num + r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; }
	public static ModInteger operator -(ModInteger l, ModInteger r) { var n = l.num + Mod - r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; }
	public static ModInteger operator *(ModInteger l, ModInteger r) { return new ModInteger(l.num * r.num); }
	public static implicit operator ModInteger(long n) { return new ModInteger(n); }
	public static ModInteger Pow(ModInteger v, long k) {
		ModInteger ret = 1;
		var n = k;
		for (; n > 0; n >>= 1, v *= v) {
			if ((n & 1) == 1)
				ret = ret * v;
		}
		return ret;
	}
}
#endregion
public class TreeDP {
	DP[] dp;
	List<int>[] G;
	public TreeDP() {
		Func<int, int, DP> dfs = null;
		dfs = (prev, cur) => {
			var ret = new DP();
			foreach (var to in G[cur])
				if (prev != to) ret += dfs(cur, to);
			return dp[cur] = !ret;
		};
		dfs(-1, 0);
		dfs = (prev, cur) => {

			var ret = new DP();
			var k = G[cur].Count;
			var rdp = new DP[k + 1];
			rdp[k] = new DP();
			for (int i = k - 1; i >= 0; i--)
				rdp[i] = rdp[i + 1] + dp[G[cur][i]];
			for (int i = 0; i < k; i++) {
				var to = G[cur][i];
				var pre = dp[to];
				dp[cur] = !(ret * rdp[i + 1]);
				ret += dp[to];
				if (prev != to) dfs(cur, to);
			}
			return dp[cur] = !ret;
		};
		dfs(-1, 0);
	}
}
public class DP {
	public ModInteger pat;
	public int sz;
	public DP() {
		//単位元を入れる
		pat = 1;
	}
	public static Func<DP, DP, bool, DP> Merge;
	public static Func<DP, DP> Root;

	public static DP operator +(DP l, DP r) { return Merge(l, r, true); }
	public static DP operator *(DP l, DP r) { return Merge(l, r, false); }
	/// <summary>
	/// 根をつける操作
	/// </summary>
	public static DP operator !(DP x) { return Root(x); }
}