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
def dfs(i):
    stack = []
    stack.append([i, []])
    while (stack):
        q, subs = stack[-1]
        size = visited[q]
        if size == 0:
            visited[q] = size = 1
            subs[:] = [elem for elem in ed[q] if visited[elem] == 0]
        if subs:
            stack.append([subs.pop(), []])
        else:
            u = stack.pop()
            if stack:
                visited[stack[-1][0]] += size
t = int(input())
for g in range(t):
    n = int(input())
    visited = [0] * (n + 1)
    stack = []
    mod = 1000000007
    ed = [[] for i in range(n + 1)]
    for i in range(n - 1):
        a, b = [int(q) for q in input().split()]
        ed[a].append(b)
        ed[b].append(a)
    m = int(input())
    f = [int(i) for i in input().split()]
    f.sort()
    dfs(1)
    if m > n - 1:
        for k in range(n - 1, m):
            f[n - 2] = f[n - 2] * f[k] % mod
            f[n - 2] %= mod;
    else:
        f = [1] * (n - 1 - m) + f
    for i in range(n + 1):
        visited[i] = visited[i] * (n - visited[i])
    visited.sort()
    res = 0
    for i in range(n - 2, -1, -1):
        res += visited[i + 2] * f[i]
        res %= mod
    print(res)
    