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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
	static final long MOD=1000000007;//998244353;
	static long[] dp1;
	static long[] dp2;
	static long[] size1;
	static long[] size2;
	static Binomial bi;
	static long[] ans;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		long M=MOD;
		graph G=new graph(N);
		for (int i = 0; i < N-1; i++) {
			int a=sc.nextInt()-1;
			int b=sc.nextInt()-1;
			G.addEdge(a, b, 1);
			G.addEdge(b, a, 1);
		}
		dp1=new long[N];
		dp2=new long[N];
		size1=new long[N];
		size2=new long[N];
		ans=new long[N];
		bi=new Binomial();
		G.dfs1(0, -1, M);
		G.dfs2(0, -1, M);
		G.dfs3(0, -1, M);
		for (int i = 0; i < ans.length; i++) {
			out.println(ans[i]);
		}
		out.flush();
 	}
	static class Binomial{
		int MAX = 510000;//ほしいサイズ
		long[] fac=new long[MAX];
		long[] finv=new long[MAX];
		long[] inv=new long[MAX];
		public Binomial(){
			fac[0] = fac[1] = 1;
		    finv[0] = finv[1] = 1;
		    inv[1] = 1;
		    for (int i = 2; i < MAX; i++){
		        fac[i] = fac[i - 1] * i % MOD;
		        inv[i] = MOD - inv[(int) (MOD%i)] * (MOD / i) % MOD;
		        finv[i] = finv[i - 1] * inv[i] % MOD;
		    }//facがx!、finvがx!の逆元,10^7くらいまでのテーブル(MAXまで)
		}
		long fac(int x) {
			return fac[x];
		}
		long invf(int x) {
			return finv[x];
		}
		long nCk(int n,int k,long MOD) {
		    if (n < k) return 0;
		    if (n < 0 || k < 0) return 0;
		    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
		}
	}
	static class graph{
		ArrayList<Edge>[] list;
		int size;
		long INF=Long.MAX_VALUE/2;
		int[] color;
		@SuppressWarnings("unchecked")
		public graph(int n) {
			size = n;
			list = new ArrayList[n];
			color =new int[n];
			for(int i=0;i<n;i++){
				list[i] = new ArrayList<Edge>();
			}
		}
		void addEdge(int from,int to,long w) {
			list[from].add(new Edge(to,w));
		}
		void dfs1(int v,int p,long M) {
			long dpmul=1L;
			long sizes=0;
			for (Edge edge: list[v]) {
				if (edge.to==p) {
					continue;
				}
				dfs1(edge.to, v,M);
				sizes+=size1[edge.to];
				dpmul*=(dp1[edge.to]*bi.invf((int)size1[edge.to]))%M;
				dpmul%=M;
			}
			size1[v]=sizes+1;
			dp1[v]=dpmul*bi.fac((int)sizes);
			dp1[v]%=M;
		}
		void dfs2(int v,int p,long M) {
			if (p==-1) {
				dp2[v]=1;
				size2[v]=0;
			}
			long[] left=new long[list[v].size()+1];
			long[] right=new long[list[v].size()+1];
			left[0]=1;
			right[right.length-1]=1;
			for (int i = 1; i < right.length; i++) {
				if (list[v].get(i-1).to==p) {
					left[i]=left[i-1];
					continue;
				}
				left[i]=(((left[i-1]*dp1[list[v].get(i-1).to])%M)*bi.invf((int)size1[list[v].get(i-1).to]))%M;
				left[i]%=M;
			}
			for (int i = right.length-2; i >= 0; i--) {
				if (list[v].get(i).to==p) {
					right[i]=right[i+1];
					continue;
				}
				right[i]=(((right[i+1]*dp1[list[v].get(i).to])%M)*bi.invf((int)size1[list[v].get(i).to]))%M;
				right[i]%=M;
			}
			for (int i = 0; i < list[v].size(); i++) {
				int to=list[v].get(i).to;
				if (to==p) {
					continue;
				}
				dp2[to]=(((((left[i]*right[i+1])%M)*(dp2[v]*bi.invf((int)size2[v]))%M)%M)*bi.fac((int)(size2[v]+size1[v]-size1[to]-1)))%M;
				size2[to]=size1[v]-size1[to]+size2[v];
				dfs2(to, v, M);
			}
		}
		void dfs3(int v,int p,long M) {
			ans[v]=(bi.invf((int)size2[v])*dp2[v])%M;
			for (Edge nv: list[v]) {
				if (nv.to==p) {
					continue;
				}
				ans[v]*=(bi.invf((int)size1[nv.to])*dp1[nv.to])%M;
				ans[v]%=M;
				dfs3(nv.to, v, M);
			}
			ans[v]*=bi.fac((int)(size1[v]-1+size2[v]));
			ans[v]%=M;
		}
	}
	
	static class Edge implements Comparable<Edge>{
		int to;
		long v;
		public Edge(int to,long v) {
			this.to=to;
			this.v=v;
		}
		@Override
    	public boolean equals(Object obj) {
    		if(obj instanceof Edge) {
    			Edge other = (Edge) obj;
    			return other.to==this.to && other.v==this.v;
    		}
    		return false;
    	}//同値の定義
    	@Override
    	public int hashCode() {
    		return Objects.hash(this.to,this.v);
    	}
    	@Override
		  public int compareTo( Edge p2 ){
			 if (this.v>p2.v) {
				return 1;
			}
			 else if (this.v<p2.v) {
				return -1;
			}
			 else {
				return 0;
			}
		  }
	} 
	static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}