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 defaultdict

mod = 10 ** 9 + 7

def dfs(node):
    ch = defaultdict(lambda :1)
    stack=[node]
    visited = [0 for i in range(n+1)]
    visited[node]=1
    for i in stack:
        for j in tree[i]:
            if not visited[j]:
                visited[j]=i
                stack.append(j)
    while len(stack)>1:
        nxt = stack.pop()
        ch[visited[nxt]] += ch[nxt]
    return sorted(ch.values())

for _ in range(int(input())):

    n= int(input())
    #Tree Creation
    tree = defaultdict(list)
    for i in range(n-1):
        u,v = map(int,input().split())
        tree[u].append(v)
        tree[v].append(u)

    children = dfs(1)

    #Prime Restoration
    k = int(input())
    primes = sorted(map(int,input().split()))
    for i in range(k-(n-1)):
        curr = primes.pop()
        primes[-1] = (curr*primes[-1])%mod
    primes = [1]*max(n-1-k,0) + primes

    #number of times a path is includes
    passage = []
    for i in range(n-1):
        passage.append((children[i])*(n-children[i]))
    passage.sort()

    ans=0
    for i,j in zip(primes,passage):
        ans+=i*j
        ans=ans%mod


    #print(*primes)
    #print(*passage)
    print(ans%mod)