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

q = 10 ** 9 + 7
T = int(sys.stdin.readline().strip())
for t in range (0, T):
    n = int(sys.stdin.readline().strip())
    N = [[] for i in range (0, n)]
    D = [0] * n
    for i in range (0, n-1):
        u, v = list(map(int, sys.stdin.readline().strip().split()))
        u, v = u - 1, v - 1
        N[u].append(v)
        N[v].append(u)
        D[u] = D[u] + 1
        D[v] = D[v] + 1
    m = int(sys.stdin.readline().strip())
    p = list(map(int, sys.stdin.readline().strip().split()))
    F = []
    M = [1] * n
    L = [i for i in range (0, n)]
    while len(L) > 0:
        L2 = []
        i = 0
        while i < len(L):
            u = L[i]
            while D[u] == 1:
                F.append(M[u] * (n - M[u]))
                D[u] = -1
                for v in N[u]:
                    if D[v] != -1:
                        D[v] = D[v] - 1
                        M[v] = M[v] + M[u]
                        if D[v] == 1:
                            u = v
            if D[L[i]] > 1:
                L2.append(i)
            i = i + 1
        L = L2[:]
    p.sort()
    F.sort()
    ans = 0
    if m <= n - 1:
        p = [1] * (n - 1 - m) + p
    else:
        for i in range (n-1, m):
            p[n-2] = (p[n-2] * p[i]) % q
    for i in range (0, n-1):
        ans = (ans + p[i] * F[i]) % q
    print(ans)

        
        