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 com.sun.javafx.geom.Edge;
import javafx.scene.effect.Effect;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.List;
import java.util.Objects;
import java.util.Queue;
import java.util.Set;
import java.util.StringTokenizer;

/**
 * http://codeforces.com/contest/1389/problem/D
 */
public class TaskD {
    public static void main(String[] arg) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        final int T = in.nextInt();
        for(int t=0;t<T;t++){
            final int n = in.nextInt();
            final Map<Integer, Set<Edge>> g = new HashMap<>();
            for(int i=1;i<=n;i++){
                g.put(i, new HashSet<>());
            }
            Map<Edge, Long> edgeMap = new HashMap<>();
            for(int i=1;i<n;i++){
                int v = in.nextInt();
                int w = in.nextInt();
                Edge e = new Edge(w, v);
                edgeMap.put(e, 0L );
                g.get(v).add(e);
                g.get(w).add(e);
            }
            final int M = in.nextInt();
            final int m[] = in.readIntArr(M);
            final long result = bfs(n,g,edgeMap, m);
            out.println(result);
        }
        out.close();
        in.close();
    }

    private static long bfs(final int n,
                     final Map<Integer, Set<Edge>> g,
                     final Map<Edge, Long> edgeMap,
                     int [] m){
        int root=0;
        for(Map.Entry<Integer, Set<Edge>> entry: g.entrySet()){
            if(entry.getValue().size()==1){
                root=entry.getKey();
            }
        }
        dfs(root, new HashSet<>(), g, edgeMap);



        long [] connections = new long[edgeMap.size()];
        int i=0;
        for(Long value:edgeMap.values()){
            connections[i]=value*(n-value);
            i++;
        }
        Arrays.sort(connections);
        Arrays.sort(m);
        final long MOD = 1_000_000_007;
        long result = 0;
        int mId = m.length-1;
        int cId = connections.length-1;
        if(mId>cId) {
            result=connections[cId];
            while (mId >= cId) {
                result *= m[mId];
                result %= MOD;
                mId--;
            }
            cId--;
        }
        for(;cId>=0;cId--){
            long me = 1;
            if(mId>=0){
                me=m[mId];
            }
            mId--;
            result+=me*connections[cId];
            result%=MOD;
        }
        return result;


//        edgeMap.forEach((k,v)->System.out.printf("%s %d%n", k.toString(), v));
    }

    private static int dfs(final int node,
                    final Set<Integer> visited,
                    final Map<Integer,Set<Edge>> g,
                    final Map<Edge, Long> edges){
        int result = 0;
        if(visited.contains(node)){
            return result;
        }
        visited.add(node);
        for(Edge edge:g.get(node)){
            int child = edge.v;
            if(child==node){
                child=edge.w;
            }
            int l = dfs(child, visited, g, edges);
            edges.put(edge, l+0L);
            result+=l;
        }
        return result+1;
    }

    private static class Edge{
        final int w;
        final int v;
        public Edge(final int w, final int v){
            this.w=w;
            this.v=v;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Edge edge = (Edge) o;
            return w == edge.w &&
                    v == edge.v;
        }

        @Override
        public int hashCode() {
            return Objects.hash(w, v);
        }

        @Override
        public String toString() {
            return String.format("( %d , %d )", w, v);
        }
    }



    private static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

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

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

        int[] readIntArr(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = Integer.parseInt(next());
            }
            return result;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        long nextLong() {
            return Long.parseLong(next());
        }

    }

}
