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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    final static int MOD = 1_000_000_000 + 7;
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int tt = sc.nextInt();
        while (tt-- > 0){
            int n = sc.nextInt();
            List<List<Integer>> tree = buildUnWeightedGraph(n, n - 1, sc);
            int m = sc.nextInt();
            LinkedList<Long> weights = new LinkedList<>();
            for(int i = 1; i <= m; ++i)
                weights.add(sc.nextLong());

            Collections.sort(weights, Collections.reverseOrder());

            while (weights.size() < n - 1)
                weights.addLast(1L);

            if(weights.size() > n - 1){
                long compositeWt = 1L;
                while (weights.size() >= n - 1){
                    compositeWt = mulMod(compositeWt, weights.removeFirst(), MOD);
                }
                weights.addFirst(compositeWt);
            }

            List<Long> edgeFreq = new ArrayList<>();
            boolean[] visited = new boolean[n];
            dfs(tree, 0, visited, n, edgeFreq);

            Collections.sort(edgeFreq, Collections.reverseOrder());

            long edgesSum = 0L;
            Iterator<Long> edgeWtIterator = weights.listIterator();
            Iterator<Long> edgeFreqIterator = edgeFreq.iterator();
            while (edgeWtIterator.hasNext()){
                long currEdgeSum = mulMod(edgeFreqIterator.next(), edgeWtIterator.next(), MOD);
                edgesSum = addMod(edgesSum, currEdgeSum, MOD);
            }

            System.out.println(edgesSum);
        }
    }

    private static long dfs(List<List<Integer>> tree, int u, boolean[] visited, int n, List<Long> edgesFreq){
        long subTreeSize = 0L;
        visited[u] = true;
        for(int v : tree.get(u)){
            if(!visited[v]){
                long childTreeSize = dfs(tree, v, visited, n, edgesFreq);
                //subTreeSize = addMod(subTreeSize, childTreeSize, MOD);
                subTreeSize += childTreeSize;
                //long timesEdgeUsed  = mulMod(childTreeSize, n - childTreeSize, MOD);
                long timesEdgeUsed  = childTreeSize * (n - childTreeSize);
                edgesFreq.add(timesEdgeUsed);
            }
        }

        return 1 + subTreeSize;
    }

    private static long mod(long x, int MOD ){
        return ((x % MOD + MOD) % MOD);
    }

    private static long addMod(long a, long b, int MOD){
        return mod(mod(a, MOD) + mod(b, MOD), MOD);
    }
    private static long mulMod(long a, long b, int MOD){
        return mod(mod(a, MOD) * mod(b, MOD), MOD);
    }

    private static List<List<Integer>> buildUnWeightedGraph(int nodes, int edges, FastReader sc){
        List<List<Integer>> graph = new ArrayList<>();
        for(int i = 1; i <= nodes; ++i)
            graph.add(new ArrayList<>());

        for(int i = 1; i <= edges; ++i){
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            graph.get(u).add(v);
            graph.get(v).add(u);
        }

        return graph;
    }
    private static class FastReader {
        private 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;
        }

        int[] readArray(int n){
            int[] arr = new int[n];
            for(int i = 0; i < n; ++i)
                arr[i] = nextInt();

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

            return arr;
        }

        double[] readDoubleArray(int n){
            double[] arr = new double[n];
            for(int i = 0; i < n; ++i)
                arr[i] = nextDouble();
            return arr;
        }

    }
}
