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
def DFS():
	stack = [1]
	visited = [0] * (n+1)
	visited[1] = 1
	par = [0] * (n+1)
	tp_stack = [1]
	
	while stack:
		new_stack = []
		for node in stack:
			for ne_node in e[node]:
				if visited[ne_node] == 0:
					visited[ne_node] = 1
					par[ne_node] = node
					new_stack.append(ne_node)
					tp_stack.append(ne_node)
		stack = list(new_stack)

	tp_stack = tp_stack[::-1]

	for node in tp_stack:
		if par[node] != 0:
			child[par[node]] += child[node]
			edge.append(child[node]*(n-child[node]))

	edge.sort()


for t in range(int(input())):
	n = int(input())

	child = [1] * (n+1)
	e = [[] for i in range(n+1)]
	edge = []
	mod = 1000000007

	for i in range(n-1):
		u,v = map(int,input().split())
		e[u].append(v)
		e[v].append(u)

	DFS()

	m = int(input())
	fac = list(map(int,input().split()))

	if m <= n-1 :
		for i in range(n-m-1):
			fac.append(1)
		fac.sort()
	else:
		fac.sort()
		for i in range(n-1,m):
			fac[n-2] *= fac[i]
			fac[n-2] %= mod

	ans = 0

	for i in range(n-2,-1,-1):
		ans += edge[i]*fac[i]
		ans%=mod

	print(ans)