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.
#!/usr/bin/env python3
import sys
input = sys.stdin.readline

MOD = 10**9 + 7

t = int(input())
for _ in range(t):
    n = int(input())
    edge = [[] for _ in range(n)]
    for _ in range(n-1):
        u, v = map(int, input().split())
        u -= 1; v -= 1
        edge[u].append(v)
        edge[v].append(u)
    m = int(input())
    pf = [int(item) for item in input().split()]

    st = []
    weight = [1] * n
    cost = []
    st.append((-1, 0, True))
    while st:
        p, v, is_decreasing = st.pop() 
        if is_decreasing:
            if p != -1:
                st.append((v, p, False))
            for nv in edge[v]:
                if nv == p:
                    continue
                st.append((v, nv, True))
        else:
            cost.append(weight[p] * (n - weight[p]))
            weight[v] += weight[p]
    cost.sort()
    pf.sort()
    ret = 0
    if len(pf) > len(cost):
        accum = 1
        for _ in range(len(pf) - len(cost)):
            accum *= pf.pop()
            accum %= MOD
        pf[-1] *= accum
    pf.reverse()
    for item in pf:
        ret += item * cost.pop()
        ret %= MOD
    ret += sum(cost)
    print(ret % MOD)