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
input = sys.stdin.readline
 
 
def dfs(tree, root):
    n = len(tree)
    visited = [False] * n
    visited[root] = True
    tp_sorted = [root]
    stack = [root]
    while stack:
        new_stack = []
        for v in stack:
            for nxt_v in tree[v]:
                if visited[nxt_v]:
                    continue
                visited[nxt_v] = True
                new_stack.append(nxt_v)
                P[nxt_v] = v
                tp_sorted.append(nxt_v)
                #print(tp_sorted, 'sorted')
        stack = list(new_stack)
    return tp_sorted, P
 
t = int(input())
for _ in range(t):
    n = int(input())
    edges = [list(map(int, input().split())) for i in range(n - 1)]
    
    tree = [[] for i in range(n)]
    for a, b in edges:
        a -= 1
        b -= 1
        tree[a].append(b)
        tree[b].append(a)
 
    root = 0
    P = [-1] * n
    tp_sort, P = dfs(tree, root)

    W = [0] * n
    
    tp_sort = tp_sort[::-1]

    for v in tp_sort:
        if P[v] != -1:
            W[P[v]] += W[v] + 1

    m = int(input())
    primes = list(map(int, input().split()))
    primes.sort(reverse=True)
    for i in range(n):
        W[i] += 1
        W[i] = W[i] * (n-W[i])
    
    W.sort(reverse=True)
    if len(primes)>n-1:
        mul = 1
        for i in range(len(primes)-n+2):
            mul *= primes[i]
            mul = mul % (10**9 + 7)
            
        primes = [mul] + primes[len(primes)-n+2:]
    
    while len(primes)<n-1:
        primes.append(1)
    
    ans = 0
    for i in range(n-1):
        ans += (W[i] * primes[i]) % (10**9+7)
    
    print(ans% (10**9+7))