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 sys import stdin, stdout
from collections import defaultdict
MOD=10**9+7

def KK(G,N):
    st=[0]
    P=[-1]*N
    P[0]=0
    for i in st:
        for j in G[i]:
            if P[j]!=-1: continue
            P[j]=i
            st.append(j)
    CH=[1]*N
    while st:
        a=st.pop()
        CH[P[a]]+=CH[a]
    return CH
        

def find(g,PR,N,m):
    ch=KK(g,N)
    arr=[]
    for i in range(1,N):
        arr.append(ch[i]*(N-ch[i]))
    PR.sort()
    arr.sort()
    while(len(PR)>len(arr)): PR.append((PR.pop()*PR.pop())%MOD)
    r=0
    while arr:
        a=arr.pop()
        b=PR.pop() if PR else 1
        r=(r+a*b)%MOD
    return r
    
def main():
    for _ in range(int(stdin.readline())):
        N=int(stdin.readline())
        g=[[] for _ in range(N)]
        for _ in range(N-1):
            a,b=list(map(int, stdin.readline().split()))
            g[a-1].append(b-1)
            g[b-1].append(a-1)
        m=int(stdin.readline())
        arr=list(map(int, stdin.readline().split()))
        print(find(g,arr,N,m))
main()