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.
t=int(input())
mod=10**9+7
from collections import deque
def pr(l):
	a=1
	for i in l:
		a=(a*i)%mod
	return(a)

def dfs():
	ch={i:1 for i in range(n)}
	par={i:-1 for i in range(n)}
	vis=[False for i in range(n)]
	s=deque([0])
	q=[]
	while s:
		x=s.popleft()
		q.append(x)
		vis[x]=True
		for y in tr[x]:
			if vis[y]:continue
			s.append(y)
			par[y]=x
			
	for i in range(n-1,0,-1):
		ch[par[q[i]]]+=ch[q[i]]
	
	l=[ch[i]*(n-ch[i]) for i in range(1,n)]
	l.sort()
	return(l)

for _ in range(t):
	n=int(input())
	tr=[[] for i in range(n)]
	for __ in range(n-1):
		u,v=map(int,input().split())
		u-=1
		v-=1
		tr[u].append(v)
		tr[v].append(u)
	m=int(input())
	k=list(map(int,input().split()))
	k.sort()

	if m>n-1:
		k=k[:n-2]+[pr(k[n-2:])]
	elif m<n-1:
		k=[1 for ii in range(n-1-m)]+k
	z=dfs()
	ans=0

	for i in range(n-1):
		ans=(ans+z[i]*k[i])%mod
	print(ans)