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.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=input.nextInt();
        while(T-->0)
        {
            int n=input.nextInt();
            ArrayList<Integer> adj[]=new ArrayList[n+1];
            Vertex V[]=new Vertex[n+1];
            for(int i=1;i<=n;i++)
            {
                adj[i]=new ArrayList<>();
                V[i]=new Vertex(i);
            }
            for(int i=0;i<n-1;i++)
            {
                int u=input.nextInt();
                int v=input.nextInt();
                adj[u].add(v);
                adj[v].add(u);
            }
            int m=input.nextInt();
            ArrayList<Long> factors=new ArrayList<>();
            for(int i=0;i<m;i++)
            {
                factors.add((long)input.nextInt());
            }
            ArrayList<Integer> list=bfs(adj,V,1);
            int arr[]=new int[n+1];
            ArrayList<Long> mul=new ArrayList<>();
            for(int i=list.size()-1;i>=0;i--)
            {
                int u=list.get(i);
                int count=0;
                for(int j=0;j<adj[u].size();j++)
                {
                    int v=adj[u].get(j);
                    if(!(V[u].parent!=null && v==V[u].parent.key))
                    {
                        count+=arr[v];
                    }
                }
                count++;
                arr[u]=count;
                if(u!=1)
                {
                    long val=(long)arr[u]*(long)(n-arr[u]);
                    mul.add(val);
                }
            }
            Collections.sort(mul);
            long mod=1000000007;
            Collections.sort(factors);
            long ans=0;
            n--;
            if(m<=n)
            {
                int j=0;
                for(int i=1;i<=n-m;i++)
                {
                    ans=(ans%mod+mul.get(j)%mod)%mod;
                    j++;
                }
                for(int i=0;i<m;i++)
                {
                    long v=(factors.get(i)%mod*mul.get(j)%mod)%mod;
                    j++;
                    ans=(ans%mod+v%mod)%mod;
                }
            }
            else
            {
                /*
                long v1=1;
                for(int i=0;i<m-n;i++)
                {
                    v1=(v1%mod*factors.get(i)%mod)%mod;
                }
                v1=(v1%mod*factors.get(factors.size()-1)%mod)%mod;
                factors.set(factors.size()-1,v1);

                 */
                int j=0;
                for(int i=0;i<n;i++)
                {
                    long v=(factors.get(i)%mod*mul.get(j)%mod)%mod;
                    if(i==n-1)
                    {
                        for(int k=n;k<m;k++)
                        {
                            v=(v%mod*factors.get(k)%mod)%mod;
                        }
                    }
                    j++;
                    ans=(ans%mod+v%mod)%mod;
                }
            }
            out.println(ans);
        }
        out.close();
    }
    public static ArrayList<Integer> bfs(ArrayList<Integer> adj[],Vertex V[], int s)
    {
        ArrayList<Integer> list=new ArrayList<>();
        V[s].color="gray";
        V[s].d=0;
        V[s].parent=null;
        Queue<Integer> q=new LinkedList<>();
        q.add(s);
        list.add(s);
        while(!q.isEmpty())
        {
            int k=q.poll();
            Vertex u=V[k];
            for(int i=0;i<adj[k].size();i++)
            {
                int key=adj[k].get(i);
                Vertex v=V[key];
                if(v.color=="white")
                {
                    q.add(key);
                    list.add(key);
                    v.color="gray";
                    v.d=u.d+1;
                    v.parent=u;
                }
            }
            u.color="black";
        }
        return list;
    }
    public static class Vertex
    {
        int key;
        int d,f;
        String color;
        Vertex parent;
        Vertex(int key)
        {
            this.key=key;
            this.d=0;
            this.f=0;
            this.color="white";
            this.parent=null;
        }
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {

            return Long.parseLong(next());
        }

        double nextDouble()
        {

            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}