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.
for t in range(int(input())):
    n = int(input())
    d = {}
    children = {}
    for i in range(n): d[i] = set()
    for i in range(n): children[i] = 0

    for i in range(n-1):
        u, v = map(int, input().split())
        d[u-1].add(v-1)
        d[v-1].add(u-1)

    child = []
    for i in d:
        if i != 0 and len(d[i]) == 1:
            child.append(i)

    p1 = []
    still = n-1

    while still != 0:
        still -= 1
        i = child.pop()
        p1.append(children[i])
        par = d[i].pop()
        children[par] += (1+children[i])
        d[par].remove(i)
        if len(d[par]) == 1 and par != 0: child.append(par)

    m1 = []
    for i in p1: m1.append((i+1)*(n-i-1))
    m1 = list(sorted(m1))[::-1]

    m = int(input())
    lm = list(map(int, input().split()))
    while len(lm) < n-1:
        lm.append(1)
    lm = list(sorted(lm))

    while len(lm) > n-1:
        new = (lm[-1]*lm[-2]) % (10**9+7)
        lm.pop()
        lm[-1] = new

    ans = 0
    for i in range(n-1):
        ans += lm[i]*m1[n-2-i]

    print(ans % (10**9+7))
