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.
//package cf665;

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.*;
import java.util.stream.Collectors;

public class D {
    static long MOD = 1_000_000_007;
    static List<Long> subtreeSizes = new ArrayList<>();

    public static void main(String[] args) throws IOException {
        Reader sc = new Reader();

        int tests = sc.nextInt();
        for (int t = 0; t < tests; t++) {
            subtreeSizes = new ArrayList<>();
            int n = sc.nextInt();
            if (n==1) {
                System.out.println(0);
                continue;
            }
            construct(n, sc);
            int m = sc.nextInt();
            LinkedList<Long> factorsList = new LinkedList<>();
            for(int i = 0; i < m; i++) {
                factorsList.add(sc.nextLong());
            }
            factorsList.sort(Comparator.reverseOrder());
            while (factorsList.size() > n - 1) {
                long prod = factorsList.poll() * factorsList.poll();
                prod %= MOD;
                factorsList.addFirst(prod);
            }
            Long[] factors = new Long[Math.min(n-1, m)];
            int j = 0;
            while(!factorsList.isEmpty()) {
                factors[j] = factorsList.poll();
                j++;
            }
//            System.out.println(Arrays.toString(factors));

            List<Long> counted = subtreeSizes.stream()
                    .map(s -> (s * (n-s)))
                    .sorted(Comparator.reverseOrder())
                    .map(s -> s % MOD)
                    .collect(Collectors.toList());
            long sum = 0L;

            for(int i = 0; i < n - 1; i++) {
                long factor = i >= factors.length ? 1 : factors[i];
                sum += ((counted.get(i) * factor) % MOD);
                sum %= MOD;
            }
            System.out.println(sum);
        }
    }

    // constructs a tree with n nodes, rooted at 1
    static Node construct(int n, Reader sc) throws IOException {
        List<List<Integer>> adj = getAdj(n, sc);
        Node root = new Node(1, null, 0);
        root.construct(adj);
        return root;
    }

    static List<List<Integer>> getAdj(int n, Reader sc) throws IOException {
        List<List<Integer>> adj = new ArrayList<>();
        for(int i = 0; i < n; i++) adj.add(new ArrayList<>());
        for(int i = 0; i < n - 1; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            adj.get(a-1).add(b);
            adj.get(b-1).add(a);
        }
        return adj;
    }

    static class Node {
        int id;
        Node parent;
        List<Node> children;
        int depth;
        int nodesInSubtree; // including self

        public Node(int id, Node parent, int depth) {
            this.id = id;
            this.parent = parent;
            this.depth = depth;
        }

        void construct(List<List<Integer>> adj) {
//            System.out.println("constructing node " + id);
            children = new ArrayList<>(adj.get(id-1)).stream()
                    .filter(v -> parent == null || v != parent.id)
                    .map(v -> new Node(v, this, depth+1))
                    .collect(Collectors.toList());
//            System.out.println("children : " + children.stream().map(i->i.id).collect(Collectors.toList()));
            int subtreeSize = 1;
            for (Node child:children) {
                child.construct(adj);
                subtreeSize += child.nodesInSubtree;
            }
            this.nodesInSubtree = subtreeSize;
            if (parent != null) {
//                System.out.printf("setting subtree size %d for node %d\n", nodesInSubtree, id);
                subtreeSizes.add((long) nodesInSubtree);
            }
        }
    }
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)
                return -ret;
            return ret;
        }
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}
