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
inp = sys.stdin.readline

mod = 10 ** 9 + 7

def solve():
	N = int(inp())
	d = [set() for _ in range(N + 1)]
	for i in range(N - 1):
		u, v = map(int, inp().split())
		d[u].add((v, i))
		d[v].add((u, i))

	G = [set() for _ in range(N + 1)]
	st = [2]
	vis = set([2])
	tp_sort = []
	while st:
		v = st.pop()
		tp_sort.append(v)
		for u, i in d[v]:
			if u in vis:
				continue
			G[v].add((u, i))
			vis.add(u)
			st.append(u)

	sz = [0] * (N + 1)
	cnt = [0] * (N - 1)
	for v in tp_sort[::-1]:
		cur = 1
		for u, i in G[v]:
			cur += sz[u]
			cnt[i] = sz[u] * (N - sz[u])
		sz[v] = cur
	
	M = int(inp())
	P = list(map(int, inp().split()))
	cnt.sort()
	cnt = cnt[::-1]
	if M <= N - 1:
		P.sort()
		P = P[::-1]
		for _ in range(N - 1 - M):
			P.append(1)
	else:
		P.sort()
		for _ in range(M - (N - 1)):
			p = P.pop()
			P[-1] = P[-1] * p % mod
		P = P[::-1]

	ans = 0
	for c, p in zip(cnt, P):
		ans = (ans + c * p) % mod
	print(ans)

for _ in range(int(input())):
	solve()
