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.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
public  class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= 1000000007;
    long fac[]= new long[3000];
    public  void solve() throws IOException 
    {
      int t = readInt();


      for(int f =0;f<t;f++)
      {
            int n = readInt();

            ArrayList<Integer> arr[]= new ArrayList[n+1];
            for(int i =1;i<=n;i++)
                arr[i]= new ArrayList<>();

            for(int i=1;i<n;i++)
            {
                int u = readInt();
                int v = readInt();
                arr[u].add(v);
                arr[v].add(u);
            }

            int m = readInt();
            ArrayList <Integer>com= new ArrayList<>();
            for(int i =0;i<m;i++)
            {
                int a= readInt();
                com.add(a);
            }

            Collections.sort(com);

            ArrayList<Long> edge= new ArrayList<>();
        
             dfs(arr,1,-1,edge);
            long ans=0;
            Collections.sort(edge);

            if(com.size()>edge.size())
            {
                for(int i =0;i<edge.size()-1;i++)
                {
                    long lp = edge.get(i);
                    lp=lp%in;
                    long go = com.get(i);
                    lp= (lp*go)%in;
                    ans = (ans%in + lp%in)%in;
                }
                long plow =edge.get(n-2);
                plow = plow%in;
                for(int i =edge.size()-1;i<com.size();i++)
                {
                      plow = (plow*com.get(i))%in;

                }
                ans = (ans%in+ plow%in)%in;
            }
            else
            {
                    for(int i =0;i<com.size();i++)
                    {
                        long lp = edge.get(edge.size()-i-1);
                        lp=lp%in;
                        long go = com.get(com.size()-i-1);
                         lp= (lp*go)%in;
                         ans = (ans%in + lp%in)%in;
                    }

                    for(int i =com.size();i<edge.size();i++)
                    {
                        long lp = edge.get(edge.size()-i-1);
                        lp=lp%in;
                       
                         ans = (ans%in + lp%in)%in;
                    }

            }
            out.println(ans);

      }      

    }
    public int dfs(ArrayList<Integer> arr[] , int u , int par , ArrayList<Long> edge)
    {
                  
                   int sum =0;
                   for(int i = 0;i<arr[u].size();i++)
                   {
                     int v = arr[u].get(i);
                     if(v!=par)
                     { 
                        int yo = dfs(arr,v,u,edge);
                        long no = arr.length-1-yo;
                        long snow = yo;
                        snow = snow*no;
                        edge.add(snow);
                        sum= sum+yo;
                     }
                   }
                   return sum+1;
    }
   
    public int value (int seg[], int left , int right ,int index, int l, int r)
    {
            
            if(left>right)
            {
              return -100000000;
            }
            if(right<l||left>r)
                return -100000000;
            if(left>=l&&right<=r)
                return seg[index];
            int mid = left+(right-left)/2;
            int val = value(seg,left,mid,2*index+1,l,r);
            int val2 = value(seg,mid+1,right,2*index+2,l,r);
            return Math.max(val,val2);

    }
   
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int val ;
    int color;
    
    edge(int u, int v)
    {
       this.val=u;
       this.color=v;
    }
    public int compareTo(edge e)
    {
        return this.val-e.val;
    }
}