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 io
import os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
mod = 10 ** 9 + 7

q = int(input())
res = []

for _ in range(q):
    n = int(input())
    E = [[] for _ in range(n + 1)]

    for i in range(n - 1):
        x, y = map(int, input().split())
        E[x].append(y)
        E[y].append(x)

    m = int(input())
    V = sorted(map(int, input().split()))

    if m < n - 1:
        V = [1] * (n - 1 - m) + V
    else:
        X = 1
        for j in range(m - n + 1):
            X = X * V[-j - 1] % mod
        V[n - 2] = V[n - 2] * X % mod

    order = []
    que = [(1, -1)]
    par = [-1] * (n + 1)
    size = [1] * (n + 1)

    while que:
        x, px = que.pop()
        order.append(x)

        for v in E[x]:
            if v == px:
                continue
            que.append((v, x))
            par[v] = x

    products = []
    order.reverse()
    for x in order:
        px = par[x]
        if px == -1:
            continue
        products.append(size[x] * (n - size[x]))
        size[px] += size[x]

    products.sort()

    ans = 0
    for i in range(n - 1):
        ans = (ans + products[i] * V[i]) % mod
    res.append(ans)
print("\n".join(map(str, res)))
