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.
'''
Name : Jaymeet Mehta
codeforces id :mj_13
Problem : 
'''
from sys import setrecursionlimit
from sys import stdin,stdout
from collections import deque
mod=int(1e9+7)
test=int(stdin.readline())
for _ in range(test):
    n=int(stdin.readline())
    graph=[[] for i in range(n)]
    for i in range(n-1):
        u,v = map(int,stdin.readline().split())
        graph[u-1].append(v-1)
        graph[v-1].append(u-1)
    m = int(stdin.readline())
    f = [int(x) for x in stdin.readline().split()]
    visited=[False for i in range(n)]
    sub=[1 for i in range(n)]
    parent=[-1 for i in range(n)]
    q=deque([0])
    bfs=[]
    visited[0]=True
    while(q):
        u=q.popleft()
        for v in graph[u]:
            if not visited[v]:
                visited[v]=True
                bfs.append(v)
                parent[v]=u
                q.append(v)
    for i in bfs[::-1]:
        sub[parent[i]]+=sub[i]
    cont=[]
    for i in range(1,n):
        ans=sub[i]*(n-sub[i])
        cont.append(ans)
    for i in range(m,n-1):
        f.append(1)
    f.sort()
    cont.sort()
    ans=0
    while(len(f)>n-1):
        f[-2]=(f[-1]*f[-2])%mod
        a=f.pop()
    for i in range(n-1):
        ans=(ans+cont[i]%mod * f[i])%mod
    print(int(ans))