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
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def main():
    t = int(input())

    for i in range(t):
        n = int(input())
        e_list = [[] for i in range(n)]
        for j in range(n-1):
            a,b = list(map(int,input().split()))
            a,b = a-1,b-1
            e_list[a].append(b)
            e_list[b].append(a)
        
        m = int(input())
        p = list(map(int,input().split()))

        from collections import deque
        
        vi = 0  #change
        INF = float('inf')
        
        Q = deque([vi])
        
        checked_list = [False]*n
        checked_list[vi]=True
        
        parent_list = [-1]*n

        min_path_list = [INF]*n #change
        min_path_list[vi] = 0
        
        while len(Q)>0:
            v = Q.pop()
            for v1 in e_list[v]:
                if not checked_list[v1]:
                    checked_list[v1]=True
                    Q.appendleft(v1)
                    parent_list[v1] = v
                    min_path_list[v1] = min_path_list[v]+1
        
        memo = [-1]*n

        min_path = [(i,min_path_list[i]) for i in range(n)]
        min_path.sort(key=lambda x:x[1],reverse=True)
        for v,d in min_path:
            if v==0:
                continue
            count = 0
            for v1 in e_list[v]:
                if v1!=parent_list[v]:
                    #print(v1)
                    count+=memo[v1]+1
            memo[v] = count
            #print(memo)
        #print(e_list)
        memo = [(memo[i]+1)*(n-memo[i]-1) for i in range(1,n)]
        memo.sort(reverse=True)
        p.sort(reverse=True)
        #print(memo)
        ans = 0
        if m<=n-1:
            for i in range(m):
                ans+=p[i]*memo[i]
                ans%=mod
            for i in range(m,n-1):
                ans+=memo[i]
                ans%=mod
        else:
            a = 1
            for i in range(m-n+2):
                a*=p[i]
                a%=mod
            ans = a*memo[0]
            ans%=mod
            for i in range(1,n-1):
                ans+=p[i+m-n+1]*memo[i]
                ans%=mod
        print(ans)

if __name__ == '__main__':
    main()

