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 com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class EU4 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args)throws Exception{
        FastReader scan=new FastReader(System.in);
        int t=1;
        t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            Node[] gr=new Node[n+1];
            for(int i=0;i<n;i++){
                gr[i+1]=new Node();
            }
            for(int i=1;i<n;i++){
                int u=scan.nextInt();
                int v=scan.nextInt();
                gr[u].ns.add(v);
                gr[v].ns.add(u);
            }
            long mod=(long)(1e9)+7;
            int m=scan.nextInt();
            Long[] ffs=new Long[m];
            for(int i=0;i<m;i++){
                ffs[i]=scan.nextLong();
            }
            Arrays.sort(ffs,Collections.reverseOrder());
            ArrayList<Long> fs=new ArrayList<>();
            int oc=0;
            if(n-1>m){
                oc=n-1-m;
            }
            long start=1;
            int in=0;
            if(m>n-1){
                for(int i=0;i<=m-n+1;i++){
                    start=(start*ffs[i])%mod;
                }
                in=m-n+2;
            }
            if(in!=0) {
                fs.add(start);
            }
            for(int i=in;i<m;i++){
                fs.add(ffs[i]);
            }
            for(int i=0;i<oc;i++){
                fs.add(1L);
            }
            ArrayList<Long> f=new ArrayList<>();
            Set<Integer> vis=new HashSet<>();
            vis.add(1);
            dfs(1,gr,vis,f);
            Collections.sort(f,Collections.reverseOrder());
            long ans=0;
            for(int i=0;i<n-1;i++){
                long fr=f.get(i);
                fr=fr%mod;
                long mu=fs.get(i);
                ans=(ans+(fr*mu)%mod)%mod;
            }
            out.println(ans);
        }
        out.flush();
        out.close();
    }
    static long dfs(int u,Node[] gr,Set<Integer> vis,ArrayList<Long> f){
        long sum=0;
        long n=gr.length-1;
        for(Integer v:gr[u].ns){
            if(!vis.contains(v)){
                vis.add(v);
                long c=dfs(v,gr,vis,f);
                f.add(c*(n-c));
                sum+=c;
            }
        }
        return sum+1;
    }
    static class Node{
        ArrayList<Integer> ns;
        Node(){
            ns=new ArrayList<>();
        }
    }
    static class FastReader {

        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;

        FastReader(InputStream is) {
            in = is;
        }

        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }

        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan()) ;
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }

        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
}
