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=1000000007
for f in range(int(input())):
    n=int(input())
    
    neig=[0]*n
    for i in range(n):
        neig[i]=[0]
    edges=[]
    for i in range(n-1):
        vertexa,vertexb=map(int,input().split())
        vertexa-=1
        vertexb-=1
        neig[vertexa][0]+=1
        neig[vertexb][0]+=1
        neig[vertexa].append(vertexb)
        neig[vertexb].append(vertexa)
        edges.append([vertexa,vertexb])
    tod=[]
    upn=[-1]*n
    dn=[1]*n
    for i in range(n):
        if neig[i][0]==1:
            tod.append(i)
    while len(tod)>0:
        x=tod.pop()
        neig[x][0]=0
        for foo in range(1,len(neig[x])):
            v=neig[x][foo]
            if neig[v][0]>0:
                neig[v][0]-=1
                upn[x]=v
                dn[v]+=dn[x]
                if neig[v][0]==1:
                    tod.append(v)
    m=int(input())
    p=list(map(int,input().split()))
    p.sort(reverse=True)
    facs=[1]*(n-1)
    if m<n:
        for i in range(m):
            facs[i]=p[i]
    else:
        diff=m-(n-1)
        for j in range(diff):
            facs[0]*=p[j]
            facs[0]%=mod
        for j in range(diff,m):
            facs[j-diff]*=p[j]
    wedgies=[0]*(n-1)
    for i in range(n-1):
        a,b=edges[i][0],edges[i][1]
        if upn[a]==b:
            wedgies[i]=dn[a]*(n-dn[a])
        else:
            wedgies[i]=dn[b]*(n-dn[b])
    wedgies.sort(reverse=True)
    sol=0
    for i in range(n-1):
        sol+=wedgies[i]*facs[i]
        sol%=mod
    print(sol)