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
import sys
input=sys.stdin.readline
t=int(input())
for ii in range(t):
    n=int(input())
    graph=defaultdict(list)
    edge=defaultdict(int)
    for i in range(n-1):
        u,v=map(int,input().split())
        graph[u].append(v)
        graph[v].append(u)
        edge[(min(u,v),max(u,v))]=0
    m=int(input())
    p=[int(i) for i in input().split() if i!='\n']
    p.sort(reverse=True)
    OBSERVE=0
    CHECK=1
    stack=[(OBSERVE,1,0)]
    count=[0]*(n+1)
    while stack:
        state,vertex,parent=stack.pop()
        if state==OBSERVE:
            stack.append((CHECK,vertex,parent))
            for child in graph[vertex]:
                if child!=parent:
                    stack.append((OBSERVE,child,vertex))
        else:
            if len(graph[vertex])==1:
                count[vertex]=1
            for child in graph[vertex]:
                if child !=parent:
                    edge[(min(child,vertex),max(child,vertex))]=count[child]*(n-count[child])
                    count[vertex]+=count[child]
            if len(graph[vertex])!=1:
                count[vertex]+=1
    #print(edge)
    rep=[]
    ans,prod=0,1
    for i in edge:
        rep.append(edge[i])
    rep.sort(reverse=True)
    diff=0
    if m>(n-1):
        diff=m-n+1
        for i in range(diff+1):
            prod*=p[i]
            prod%=(10**9+7)
            #print(diff,prod)
    else:
        prod=p[0]
    ans+=(prod*rep[0])%(10**9+7)
    #print(ans,rep,p,prod,diff,len(rep))
    for i in range(1,len(rep)):
        if i>=len(p):
            ans+=rep[i]
            ans%=(10**9+7)
            
        else:
            ans+=(p[i+diff]*rep[i])
            ans%=(10**9+7)
    sys.stdout.write(str(ans)+'\n')
        
            
            
        
         
    
