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.
// package CodeForces;

import java.io.BufferedOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.LinkedList;

public class Round665D {

	public static final long mod = (long)1e9 + 7;
	
	public static LinkedList<Edge>[] adj;
	public static int n;
	
	public static int dfs(int curr, int pr) {
		int size = 0;
		for(Edge x : adj[curr]) {
			if(x.u == curr) {
				if(x.v != pr) {
					int tempsize = dfs(x.v, curr);
					x.wt = (long)tempsize * (long)(n - tempsize);
					size += tempsize;
				}
			}else {
				if(x.u != pr) {
					int tempsize = dfs(x.u, curr);
					x.wt = (long)tempsize * (long)(n - tempsize);
					size += tempsize;
				}
			}
		}
		return size + 1;
	}
	
	public static void solve() {
		int t = s.nextInt();
		while(t-- > 0) {
			n = s.nextInt();
			adj = new LinkedList[n];
			Edge[] e = new Edge[n - 1];
			for(int i = 0; i < n; i++) {
				adj[i] = new LinkedList<Edge>();
			}
			for(int i = 0; i < n - 1; i++) {
				int u = s.nextInt() - 1;
				int v = s.nextInt() - 1;
				e[i] = new Edge(u, v);
				adj[u].add(e[i]);
				adj[v].add(e[i]);
			}
			dfs(0, 0);
			int m = s.nextInt();
			ArrayList<Long> factors = new ArrayList<Long>();
			for(int i = 0; i < m; i++) {
				factors.add(s.nextLong());
			}
			Collections.sort(factors);
			if(m > n - 1) {
				ArrayList<Long> temp = new ArrayList<Long>();
				for(int i = 0; i < n - 2; i++) {
					temp.add(factors.get(i));
				}
				long val = 1;
				for(int i = n - 2; i < factors.size(); i++) {
					val *= factors.get(i);
					val %= mod;
				}
				temp.add(val);
				factors = temp;
			}
			Arrays.parallelSort(e);
			int ptr = factors.size() - 1;
			long ans = 0;
			for(int i = 0; i < n - 1; i++) {
				long curr = ptr < 0 ? 1 : factors.get(ptr--);
				ans += (curr * e[i].wt)%mod;
				if(ans >= mod) ans -= mod;
			}
			out.println(ans);
		}
	}

	public static class Edge implements Comparable<Edge>{
		int u;
		int v;
		long wt;
		public Edge(int u, int v) {
			this.u = u;
			this.v = v;
		}
		
		public int compareTo(Edge x) {
			return Long.compare(x.wt, this.wt);
		}
	}
	
	public static void main(String[] args) {
		new Thread(null, null, "Thread", 1 << 27) {
			public void run() {
				try {
					out = new PrintWriter(new BufferedOutputStream(System.out));
					s = new FastReader(System.in);
					solve();
					out.close();
				} catch (Exception e) {
					e.printStackTrace();
					System.exit(1);
				}
			}
		}.start();
	}

	public static PrintWriter out;
	public static FastReader s;

	public static class FastReader {

		private InputStream stream;
		private byte[] buf = new byte[4096];
		private int curChar, snumChars;

		public FastReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (snumChars == -1) {
				throw new InputMismatchException();
			}
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException E) {
					throw new InputMismatchException();
				}
			}
			if (snumChars <= 0) {
				return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int number = 0;
			do {
				number *= 10;
				number += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return number * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			long sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long number = 0;
			do {
				number *= 10L;
				number += (long) (c - '0');
				c = read();
			} while (!isSpaceChar(c));
			return number * sgn;
		}

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = this.nextInt();
			}
			return arr;
		}

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

		public String next() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndofLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public boolean isEndofLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}

	
}
