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.InputStreamReader;
import java.util.*;
import java.util.stream.Collectors;

public class Main {

    public static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws Exception {
        long t = readInt();
        while(t-->0) {
            int n = readInt();
            int[][] a = new int[n][2];
            int[] m = new int[n+1];
            Map<Integer, Set<Integer>> ad = new HashMap<>();
            for (int i = 0; i < n - 1; i++) {
                a[i] = readIntArray();
                m[a[i][0]]++;
                m[a[i][1]]++;
                ad.putIfAbsent(a[i][0], new HashSet<>());
                ad.putIfAbsent(a[i][1], new HashSet<>());
                ad.get(a[i][0]).add(a[i][1]);
                ad.get(a[i][1]).add(a[i][0]);
            }
            int[] s = new int[n+1];
            for (int i = 0; i < n + 1; i++) {
                s[i]=1;
            }
            long mod = 1000000007;
            LinkedList<Integer> q = new LinkedList<>();
            for (int i = 1; i < n+1; i++) {
                if(ad.get(i).size()==1) {
                    q.add(i);
                }
            }
            List<Long> list = new ArrayList<>();
            while(!q.isEmpty()) {
                int l = q.remove();
                if(ad.get(l).size()==0) {
                    break;
                }
                else if(ad.get(l).size()==1) {
                    long tv = ((long)s[l]*(long)(n-s[l]));
                    list.add(tv);
                    int ne=0;
                    for(Integer i : ad.get(l)) {
                        ne = i;
                    }
                    s[ne] += s[l];
                    ad.get(ne).remove(l);
                    ad.get(l).remove(ne);
                    if(ad.get(ne).size()==1) {
                        q.add(ne);
                    }
                }
            }
            /*for (long i = 1; i <= n ; i++) {
                System.out.print(s[i] + " ");
            }
            System.out.println();
            for (long i = 0; i < list.size(); i++) {
                System.out.println(list.get(i) + " ");
            }
            System.out.println();*/
            Collections.sort(list);
            int p = readInt();
            long[] k = readLongArray();
            Arrays.sort(k);
            long[] nk = new long[p];
            for (int i = 0; i < p; i++) {
                nk[i] = k[p-i-1];
            }
            long ans = 0;
            int size = list.size();
            if(k.length<=size-1) {
                for (int i = size-1; i >=0; i--) {
                    if(size-i-1<k.length) {
                        ans = ans + list.get(i)*nk[size-i-1];
                        ans = ans%mod;
                    }
                    else {
                        ans = ans + list.get(i);
                        ans = ans%mod;
                    }
                }
            }
            else {
                for (int i = size-2; i >=0; i--) {
                    if(size-i-1<k.length) {
                        ans = ans + list.get(i)*k[i];
                        ans = ans%mod;
                    }
                }
                long tt = 1;
                for (int i = size-1; i < k.length; i++) {
                    tt = tt*k[i];
                    tt = tt%mod;
                }
                ans = ans + tt*list.get(size-1);
                ans = ans%mod;
            }
            System.out.println(ans);

        }
    }

    private static String readString() throws Exception {
        return br.readLine();
    }

    private static int readInt() throws Exception{
        return Integer.parseInt(readString());
    }

    private static long readLong() throws Exception{
        return Long.parseLong(readString());
    }

    private static double readDouble() throws Exception{
        return Double.parseDouble(readString());
    }

    private static String[] readStringArray() throws Exception {
        return br.readLine().split(" ");
    }

    private static List<String> readStringList() throws Exception {
        return Arrays.asList(readStringArray());
    }

    private static List<Integer> readIntList() throws Exception {
        return readStringList().stream().map(s -> Integer.parseInt(s)).collect(Collectors.toList());
    }

    private static int[] readIntArray() throws Exception {
        return readIntList().stream().mapToInt(i -> i).toArray();
    }

    private static List<Long> readLongList() throws Exception {
        return readStringList().stream().map(s -> Long.parseLong(s)).collect(Collectors.toList());
    }

    private static long[] readLongArray() throws Exception {
        return readLongList().stream().mapToLong(i -> i).toArray();
    }

    private static List<Double> readDoubleList() throws Exception {
        return readStringList().stream().map(s -> Double.parseDouble(s)).collect(Collectors.toList());
    }

    private static double[] readDoubleArray() throws Exception {
        return readDoubleList().stream().mapToDouble(i -> i).toArray();
    }
}