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,threading
def dfs(curr,prev):
    sz[curr]=1
    for i in graph[curr]:
        if i!=prev:
            dfs(i,curr)
            sz[curr]+=sz[i]
        
def main():
    for _ in range (int(input())):
        n=int(input())
        global graph
        graph = [[] for i in range (n)]
        for i in range (n-1):
            uu,vv=[int(i)-1 for i in input().split()] 
            graph[uu].append(vv)
            graph[vv].append(uu)
        m = int(input())
        p = [int(i) for i in input().split()]
        p.sort()
        global sz 
        sz = [0]*(n)
        dfs(0,0)
        c = []
        mod = 10**9 + 7
        for i in sz[1:]:
            c.append((i)*(n-i))
        c.sort()
        ans = 0
        while len(p)>len(c):
            temp = p.pop()
            p[-1]*= temp
            p[-1]%= mod
        for i in range(n-2,-1,-1):
            if len(p)>0:
                ans+= p.pop() * c.pop()
                ans%= mod
            else:
                ans+= c.pop()
                ans%= mod
        print(ans)
    
sys.setrecursionlimit(10**6)
threading.stack_size(10**8)
t = threading.Thread(target= main)
t.start()
t.join()