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.
import sys
from collections import defaultdict,deque
def bfs(node):
    q=deque([node])
    vis[node]=1
    res=[]
    while q:
        x=q.popleft()
        vis[x]=1
        res.append(x)
        for j in edge[x]:
            if vis[j]==0:
                child[x].append(j)
                q.append(j)
    res.reverse()
    return res
t=int(input())
for _ in range(t):
    n=int(input())
    z=(10**9)+7
    edge=defaultdict(list)
    child=defaultdict(list)
    for j in range(n-1):
        u,v=list(map(int,input().split()))
        edge[u].append(v)
        edge[v].append(u)
    m=int(input())
    arr=list(map(int,input().split()))
    vis=[0]*(n+1)
    subTreeSize=[1]*(n+1)
    res=bfs(1)
    for i in res:
        for j in child[i]:
            subTreeSize[i]+=subTreeSize[j]
    num=[]
    for i in res:
        for j in child[i]:
            num.append(subTreeSize[j]*(n-subTreeSize[j]))
    num.sort(reverse=True)
    arr.sort(reverse=True)
    a=n-1-len(arr)
    if a>0:
        for i in range(a):
            arr.append(1)
    else:
        for i in range(1,abs(a)+1):
            arr[0]*=arr[i]
            arr[0]%=z
    ans=0
    if a>0:
        for i in range(n-1):
            ans+=(arr[i]*num[i])
            ans%=z
    else:
        for i in range(n-1):
            if i==0:
                ans+=(arr[i]*num[i])
                ans%=z
            else:
                ans+=(arr[i+abs(a)]*num[i])
                ans%=z
    print(ans)