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.
from sys import stdin
from collections import *


class graph:
    # initialize graph
    def __init__(self, gdict=None):
        if gdict is None:
            gdict = defaultdict(list)
        self.gdict, self.edges, self.l = gdict, [], defaultdict(int)

    # add edge
    def addEdge(self, node1, node2, w=None):
        self.gdict[node1].append(node2)
        self.gdict[node2].append(node1)
        self.edges.append((node1, node2))

    def subtree(self, v):
        queue, visit, ans = deque([v]), [0] * (n + 1), [[v, 0]]
        visit[v], self.nodes = 1, [0] * (n + 1)

        while queue:
            s = queue.popleft()

            for i in self.gdict[s]:
                if not visit[i]:
                    queue.append(i)
                    visit[i] = 1
                    ans.append([i, s])

        tem = []
        for i, j in ans[::-1]:
            self.nodes[j] += self.nodes[i] + 1
            tem.append((self.nodes[i] + 1) * (n - (self.nodes[i] + 1)))

        tem.sort()
        # print(tem, p)
        ans = 0
        for i in range(n - 1):
            ans = add(ans, mult(tem[i + 1], p[i]))

        return ans


rint = lambda: int(stdin.readline())
rints = lambda: [int(x) for x in stdin.readline().split()]
add = lambda a, b: (a + b) % mod
mult = lambda a, b: ((a % mod) * (b % mod)) % mod
mod = 10 ** 9 + 7
out = []

for _ in range(int(input())):
    n = rint()
    g = graph()
    for _ in range(n - 1):
        u, v = rints()
        g.addEdge(u, v)

    m = rint()
    p = sorted(rints() + [1 for _ in range(n - 1 - m)])
    for i in range(m - (n - 1)):
        p[-2] = mult(p[-1], p[-2])
        p.pop()

    out.append(g.subtree(1))

print('\n'.join(map(str, out)))
