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.
from collections import deque

MOD = 1000000007
T = int(input())
for _ in range(T):
    n = int(input())
    e = [ [] for _ in range(n+1) ]
    for _ in range(n-1):
        a, b = map(int, input().split())
        e[a].append(b)
        e[b].append(a)

    m = int(input())
    p = list(sorted(map(int, input().split())))
    if m < n-1:
        p = [1]*(n-1-m) + p
    else:
        tp = []
        for u in p:
            if len(tp) < n-1: tp.append(u)
            else: tp[-1] = (tp[-1]*u)%MOD
        p = tp

    q, par, order = deque([1]), [0]*(n+1), []
    while q:
        u = q.popleft()
        order.append(u)
        for v in e[u]:
            if v == par[u]: continue
            par[v] = u
            q.append(v)
    
    lcc, ecc = [0]*(n+1), []
    for u in reversed(order):
        cc = 1
        for v in e[u]:
            if v == par[u]: continue
            cc += lcc[v]
        lcc[u] = cc
        if u != 1: ecc.append(cc*(n-cc))
    ecc.sort()
    
    res = 0
    for u, v in zip(p, ecc):
        res = (res + (u*v))%MOD
    print(res)


