You are given a tree that consists of n nodes. You should label each of its n-1 edges with an integer in such way that satisfies the following conditions: 

  * each integer must be greater than 0; 
  * the product of all n-1 numbers should be equal to k; 
  * the number of 1-s among all n-1 integers must be minimum possible. 



Let's define f(u,v) as the sum of the numbers on the simple path from node u to node v. Also, let ∑_{i=1}^{n-1} ∑_{j=i+1}^n f(i,j) be a distribution index of the tree.

Find the maximum possible distribution index you can get. Since answer can be too large, print it modulo 10^9 + 7.

In this problem, since the number k can be large, the result of the prime factorization of k is given instead.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines describes an edge: the i-th line contains two integers u_i and v_i (1 ≤ u_i, v_i ≤ n; u_i ≠ v_i) — indices of vertices connected by the i-th edge.

Next line contains a single integer m (1 ≤ m ≤ 6 ⋅ 10^4) — the number of prime factors of k.

Next line contains m prime numbers p_1, p_2, …, p_m (2 ≤ p_i < 6 ⋅ 10^4) such that k = p_1 ⋅ p_2 ⋅ … ⋅ p_m.

It is guaranteed that the sum of n over all test cases doesn't exceed 10^5, the sum of m over all test cases doesn't exceed 6 ⋅ 10^4, and the given edges for each test cases form a tree.

Output

Print the maximum distribution index you can get. Since answer can be too large, print it modulo 10^9+7.

Example

Input


3
4
1 2
2 3
3 4
2
2 2
4
3 4
1 3
3 2
2
3 2
7
6 1
2 3
4 6
7 3
5 1
3 6
4
7 5 13 3


Output


17
18
286

Note

In the first test case, one of the optimal ways is on the following image:

<image>

In this case, f(1,2)=1, f(1,3)=3, f(1,4)=5, f(2,3)=2, f(2,4)=4, f(3,4)=2, so the sum of these 6 numbers is 17.

In the second test case, one of the optimal ways is on the following image:

<image>

In this case, f(1,2)=3, f(1,3)=1, f(1,4)=4, f(2,3)=2, f(2,4)=5, f(3,4)=3, so the sum of these 6 numbers is 18.

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
import java.util.Stack;

public class Round659 {

	static int rec = 0;
	static int X[] = { -1, 0, 0, 1 };
	static int Y[] = { 0, -1, 1, 0 };
	static long mod=1000000007;
	static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[64]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}

	public static long[] initArray(int n, Reader scan) throws IOException {

		long arr[] = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = scan.nextLong();
		}

		return arr;
	}

	public static long sum(long arr[]) {

		long sum = 0;
		for (long i : arr) {
			sum += (long) i;
		}

		return sum;
	}

	public static long max(long arr[]) {

		long max = Long.MIN_VALUE;

		for (long i : arr) {
			max = Math.max(i, max);
		}

		return max;
	}

	public static long min(long arr[]) {
		long min = Long.MAX_VALUE;

		for (long i : arr) {
			min = Math.min(i, min);
		}

		return min;
	}

	public static List<Integer>[] initAdjacency(int n, int e, Reader scan, boolean type) throws IOException {

		List<Integer> adj[] = new ArrayList[n + 1];

		for (int i = 0; i < e; i++) {
			int u = scan.nextInt();
			int v = scan.nextInt();

			if (adj[u] == null)
				adj[u] = new ArrayList<>();
			if (type && adj[v] == null)
				adj[v] = new ArrayList<>();

			adj[u].add(v);

			if (type)
				adj[v].add(u);

		}

		return adj;
	}

	public static void main(String[] args) throws IOException {

		Reader scan = new Reader();
//		Scanner scan=new Scanner(System.in);

		int t = scan.nextInt();
		while (t-- > 0) {

//			int n = scan.nextInt();
//			int k=scan.nextInt();
//			long k=scan.nextLong();
//			int d=scan.nextInt();
//			int m=scan.nextInt();
//			int m=scan.nextInt();
//			int k=scan.nextInt();
//			int l=scan.nextInt();
//			int arr[]=new int[n];
//			
//			for(int i=0;i<n;i++) {
//				arr[i]=scan.nextInt();
//			}
//			

//			int arr1[]=new int[n];
//
//			int arr2[]=new int[m];
//			
//			for(int i=0;i<n;i++) {
//				arr1[i]=scan.nextInt();
//			}
//			
//			for(int i=0;i<m;i++) {
//				arr2[i]=scan.nextInt();
//			}
			
//			long arr[]=initArray(n, scan);
//			long x1=scan.nextLong();
//			long y1=scan.nextLong();
//			long z1=scan.nextLong();
//			long x2=scan.nextLong();
//			long y2=scan.nextLong();
//			long z2=scan.nextLong();
//			B(x1, y1, z1, x2, y2, z2);
			
			D(scan);
		}

	}
	
	
	public static void A(int n, int k) {
		
		long ans=0;
		
		if(k%2==0) {
			
			if(n%2!=0) {
				ans++;
				n++;
			}
			
		}else {
		
			if(n%2==0) {
				ans++;
				n++;
			}
		}
			
		while(k>n) {
			ans+=2;
			n+=2;
		}
		
		System.out.println(ans);
		
		
		
	}
	
	public static void B(long x1, long y1, long z1, long x2, long y2, long z2) {
		
		
		long min= Math.min(x1, z2);
		x1-=min;
		z2-=min;
		
		min=Math.min(z2, z1);
		z1-=min;
		z2-=min;
		
		long ans=0;
		min=Math.min(z1, y2);
		
		ans+= min*(long)2;
		
		z1-=min;
		y2-=min;
		
		ans-= z2*(long)2;
		System.out.println(ans);
		
		
		
	}
	
	public static void C(int n, long arr[]) {
		
		long temp[]=new long[n];
		
		for(int i=0;i<n;i++) {
			temp[i]=arr[i];
		}
		
		Arrays.sort(temp);
		
		long min=temp[0];
		
		for(int i=0;i<arr.length;i++) {
			
			if(arr[i]!=temp[i]&&(arr[i]%min!=0)) {
				System.out.println("NO");
				return;
			}
			
		}
		
		System.out.println("YES");
		
		
	}
	
	public static void D(Reader scan) throws IOException {
		
		
		int n=scan.nextInt();
		
		List<Integer> adj[]=initAdjacency(n, n-1, scan, true);
		
		int m=scan.nextInt();
		Long primes[]=new Long[m];
		
		for(int i=0;i<m;i++) {
			primes[i]=scan.nextLong();
		}
		
		
		List<Long> vals=new ArrayList<>();
		count(adj, 1, 0, vals, n);
		
		Collections.sort(vals, Collections.reverseOrder());
		
		Arrays.sort(primes, Collections.reverseOrder());
		
//		System.out.println(Arrays.toString(vals.toArray()));
//		System.out.println(Arrays.toString(primes));
		
		
		int extra= Math.max(0,  primes.length-vals.size());
		long ans=0;
		int i=0;
		long prod=1;
		for(;i<=extra;i++) {
			prod*= primes[i];
			prod%=mod;
		}
		
		ans+= (vals.get(0)*prod)%mod;
		ans%=mod;
		
		int j=1;
		
		for(;i<primes.length;i++) {
			
			ans+= (vals.get(j)*primes[i])%mod;
			ans%=mod;
			j++;
		}
		
		while(j<vals.size()) {
			ans+= ((vals.get(j))%mod);
			j++;
			ans%=mod;
		}
		
		System.out.println(ans);
		
		
		
		
	}
	
	public static long count(List<Integer> adj[], int i, int parent, List<Long> vals, int n) {
		
		
		long ans=1;
		
		for(Integer x: adj[i]) {
			if(x==parent) continue;
			
			long recAns= count(adj, x, i, vals, n);
			vals.add(recAns*(long)(n-recAns));
			ans+= recAns;
		}
		
		return ans;
		
		
	}

}
