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.
mod = 1000000007

for _ in range(int(input())):
    n = int(input())
    
    routesges = [[] for i in range(n+1)]
    for i in range(n-1):
        u, v = map(int, input().split())
        routesges[u].append([v, 0])
        routesges[v].append([u, 0])

    m = int(input())
    p = list(map(int, input().split()))
    p.sort(reverse=True)
    
    stack_1 = [[1, -1]]
    stack_2 = []
    while stack_1:
        now, parent = stack_1.pop()
        for i in range(len(routesges[now])):
            if routesges[now][i][0] != parent:
                stack_1.append([routesges[now][i][0], now])
                stack_2.append([routesges[now][i][0], now])
    
    routes = [0]*(n+1)
    while stack_2:
        to, fr_om = stack_2.pop()
        routes[to] += 1
        routes[fr_om] += routes[to]
    routes = routes[2:]
    for i in range(n-1):
        routes[i] *= (n - routes[i])
    routes.sort(reverse=True)
    
    summa = 0
    if m > n-1:
        for i in range(m-n+2):
            routes[0] = (routes[0] * p[i]) % mod
        summa = routes[0]
        for i in range(1, n-1):
            summa = (summa + routes[i] * p[i + m - n + 1]) % mod
        print(summa % mod)
    else:
        for i in range(m):
            summa = (summa + routes[i] * p[i]) % mod
        for i in range(m, n-1):
            summa = (summa + routes[i]) % mod
        print(summa % mod)
