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.
tests = int(input())
for t in range(tests):
    n = int(input())
    node_dict = {}
    for _ in range(n-1):
        u, v = list(map(int, input().split()))
        if u in node_dict:
            node_dict[u][0] += 1
            node_dict[u][1].add(v)
        else:
            node_dict[u] = [1,set([v])]
        if v in node_dict:
            node_dict[v][0] += 1
            node_dict[v][1].add(u)
        else:
            node_dict[v] = [1, set([u])]
    num_primes = int(input())
    prime_ls = sorted(list(map(int, input().split())))
    
    edge_weight = []
    visit_node = [True for _ in range(0, n+1)]
    other_node = list(node_dict[1][1])[0]
    stack = [[1, 0], [other_node,0]]
    visit_node[1] = True
    node_dict[1][0] -= 1
    node_dict[1][1].remove(other_node)
    node_dict[other_node][0] -= 1
    node_dict[other_node][1].remove(1)
    while stack:
        curr, excess = stack[-1]
        visit_node[curr] = False
        if node_dict[curr][0] == 0:            
            stack.pop()
            if stack:
                edge_weight.append((n-excess-1)*(excess+1))
                stack[-1][1] += 1 + excess
        else:
            new_node = node_dict[curr][1].pop()
            node_dict[curr][0] -= 1
            while (node_dict[curr][0] != 0) and (not visit_node[new_node]) :
                new_node = node_dict[curr][1].pop()
                node_dict[curr][0] -= 1
            if visit_node[new_node]:
                stack.append([new_node, 0])
    
    edge_weight = sorted(edge_weight)
    res = 0
    if num_primes > (n-1):
        prod = 1
        for idx in range(num_primes-1,n-3,-1):
            prod *= prime_ls[idx]
            prod = prod % (1000000007)
        prime_ls[n-2] = prod
        for idx in range(n-1):
            res += (edge_weight[idx] * prime_ls[idx]) % (1000000007)
            res = res % (1000000007)
    else:
        start_idx = n-2
        for idx in range(num_primes-1, -1, -1):
            res += edge_weight[start_idx] * prime_ls[idx]
            res = res % (1000000007)
            start_idx -= 1
        for idx in range(start_idx+1):
            res += edge_weight[idx] 
            res = res % (1000000007)
    print(res % (1000000007))
    

        
            
                
    
                    
                