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 time

if __name__=="__main__":
	for i in range(int(input())):
		#start = time.time()
		n = int(input())
		tree = [[] for j in range(n)]
		paths = [0]*n
		degree = [1]*n
		branches = [0]*n

		for j in range(n-1):
			u, v = map(int, input().split())
			tree[u-1].append(v-1)
			tree[v-1].append(u-1)
			branches[u-1]+=1
			branches[v-1]+=1
		#print("setup in", time.time()-start)
		#start = time.time()
		k=0
		for j in range(n-1):
			if degree[j]==1:
				v = j
				new_v=v
				while branches[v]==1:
					paths[k] = degree[v]
					k+=1
					for vertex in tree[v]:
						if branches[vertex]!=1:
							new_v=vertex
							break
					if new_v==v: break
					branches[new_v]-=1
					degree[new_v]+=degree[v]
					v = new_v
		#print("traversed tree in", time.time()-start)
		#start = time.time()
		m = int(input())
		labels = sorted(list(map(int, input().split())))
		if m<n:
			labels = [1]*(n-1-m)+labels
		else:
			for element in labels[n-1:]:
				labels[n-2]=(labels[n-2]*element)%(10**9+7)
		paths.pop()
		paths=[item*(n-item) for item in paths]
		paths.sort()
		#print(paths)
		#print(labels)
		print(sum([paths[j]*labels[j] for j in range(n-1)])%(10**9+7))
		#print("finished in", time.time()-start)
