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
input = sys.stdin.readline
mod=10**9+7

t=int(input())
for tests in range(t):
    n=int(input())
    E=[[] for i in range(n+1)]

    for i in range(n-1):
        x,y=map(int,input().split())
        E[x].append(y)
        E[y].append(x)

    m=int(input())
    V=sorted(map(int,input().split()))

    if m<n-1:
        V=[1]*(n-1-m)+V
    else:
        X=1
        for j in range(m-n+1):
            X=X*V[-j-1]%mod
        V[n-2]=V[n-2]*X%mod

    TOP_SORT=[]
    Q=[1]
    USE=[0]*(n+1)
    USE[1]=1
    P=[-1]*(n+1)
    
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        
        for to in E[x]:
            if USE[to]==0:
                Q.append(to)
                P[to]=x
                USE[to]=1

    L=[1]*(n+1)

    LIST=[]
    for x in TOP_SORT[1:][::-1]:
        LIST.append(L[x]*(n-L[x]))
        L[P[x]]+=L[x]

    LIST.sort()

    #print(V)
    #print(LIST)

    ANS=0
    for i in range(n-1):
        ANS=(ANS+LIST[i]*V[i])%mod
    print(ANS)
        
        
        

    
                
            
    
        

    
