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 sys
from array import array  # noqa: F401
import typing as Tp  # noqa: F401


def input():
    return sys.stdin.buffer.readline().decode('utf-8')


def output(*args):
    sys.stdout.buffer.write(
        ('\n'.join(map(str, args)) + '\n').encode('utf-8')
    )


def main():
    t = int(input())
    ans_a = []
    mod = 10**9 + 7

    for ti in range(t):
        n = int(input())
        adj = [[] for _ in range(n)]
        edge_i = [[] for _ in range(n)]
        deg = [0] * n
        for ei, (u, v) in enumerate(map(int, input().split()) for _ in range(n - 1)):
            adj[u - 1].append(v - 1)
            adj[v - 1].append(u - 1)
            edge_i[u - 1].append(ei)
            edge_i[v - 1].append(ei)
            deg[u - 1] += 1
            deg[v - 1] += 1

        m = int(input())
        p = sorted(map(int, input().split()))

        path_cnt = []
        visited_edge = [0] * (n - 1)
        stack = [i for i in range(n) if deg[i] == 1]
        size = [1] * n

        while stack:
            v = stack.pop()
            for dest, ei in zip(adj[v], edge_i[v]):
                if visited_edge[ei]:
                    continue
                visited_edge[ei] = 1
                path_cnt.append(size[v] * (n - size[v]))

                if deg[dest] == 0:
                    continue
                size[dest] += size[v]
                deg[dest] -= 1
                if deg[dest] == 1:
                    stack.append(dest)

        path_cnt.sort()
        while len(p) > n - 1:
            p[-1] = p.pop() * p[-1] % mod

        ans = 0
        while p:
            ans += path_cnt.pop() * p.pop() % mod

        ans = (ans + sum(path_cnt)) % mod
        ans_a.append(ans)

    output(*ans_a)


if __name__ == '__main__':
    main()
