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.
r = 10 ** 9 + 7



for _ in range(int(input())):
    
    N = int(input())
    
    V = [[] for i in range(N)]
    
    for i in range(N - 1):
        
        u, v = map(int, input().split())
        
        V[u - 1] += [v - 1]
        
        V[v - 1] += [u - 1]
    
    
    C = [[] for i in range(N)]
    
    P = [0] * N
    
    visited = [0] * N
    
    que = [0]
    
    visited[0] = 1
    
    while que:
        
        q = que.pop()
        
        for v in V[q]:
            
            if visited[v] == 0:
                
                visited[v] = 1
                
                C[q] += [v]
                
                P[v] = q
                
        que += C[q]
        
    que = [0]
    
    note = [1] * N
    
    while que:
        
        q = que.pop()
        
        if C[q]:
            
            que += [C[q].pop()]
            
        else:
            
            if q == 0:
                
                break
            
            note[P[q]] += note[q]
            
            que += [P[q]]
        
    
    
    
    for i in range(N):
        
        note[i] = note[i] * (N - note[i])
        
    note.sort()
    
    m = int(input())
    
    p = [1] * max(1, N - m) + list(map(int, input().split()))
    
    p.sort()
    
    for i in range(N, m + 1):
        
        p[N - 1] *= p[i]
        
        p[N - 1] %= r
        
    
    ans = 0
    for i in range(N):
        
        ans += p[i] * (note[i] % r) % r
        
        ans %= r
        
        
    print(ans)