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 itertools import repeat
def solve():
    n = int(stdin.readline())
    e = [[] for _ in xrange(n)]
    for _ in xrange(n - 1):
        x, y = stdin.readline().split()
        x = int(x, 10) - 1
        y = int(y, 10) - 1
        e[x].append(y)
        e[y].append(x)
    st = [0]
    col = [None] * n
    po = st.pop
    pu = st.append
    g = []
    while st:
        x = po()
        if col[x] is None:
            col[x] = 0
            pu(x)
            for y in e[x]:
                if col[y] is None:
                    pu(y)
        else:
            col[x] = 1
            for y in e[x]:
                if col[y]:
                    g.append(col[y] * (n - col[y]))
                    col[x] += col[y]
    m = int(stdin.readline())
    p = map(int, stdin.readline().split(), repeat(10, m))
    if m < n - 1:
        p += [1] * (n - 1 - m)
        m = n - 1
    p.sort()
    mod = 1000000007
    for i in xrange(n - 1, m):
        p[n-2] = p[n-2] * p[i] % mod
    g.sort()
    ans = 0
    for x, y in zip(p, g):
        ans = (ans + x * y) % mod
    print ans
T = int(stdin.readline())
for _ in xrange(T):
    solve()
