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 collections import defaultdict, deque
from sys import stdin
mod = 10 ** 9 + 7

for _ in range(int(input())):
    # Take the input
    n = int(input())
    adj = defaultdict(set)
    for i in range(n - 1):
        x, y = map(int, stdin.readline().split())
        x -= 1
        y -= 1
        adj[x].add(y)
        adj[y].add(x)
    m = int(input())
    k = list(map(int, stdin.readline().split()))
    k.sort()
    # Store the leaf nodes in q
    q = deque()
    for x in adj:
        if len(adj[x]) == 1:
            q.append(x)
    # Each edge counted once
    count = [1] * n
    # loop to count the count the count of each edge. COunt of parent edge is its count+count of its childs
    while len(q) > 1:
        u = q.popleft()
        baap = adj[u].pop()
        count[baap] += count[u]
        adj[baap].remove(u)
        if len(adj[baap]) == 1:
            q.append(baap)
    # Total count
    for i, j in enumerate(count):
        count[i] = j * (n - j)
    # Sort the count
    count.sort()
    count = count[1:]
    # Arrange the k's
    if m < n - 1:
        k = [1] * (n - 1 - m) + k
    elif m > n - 1:
        # When no fo factors in more than the no of edges, just multiply the greater factord to a single one
        t = 1
        for i in range(n - 2, m):
            t = (t * k[i]) % mod
        k = k[:n - 2] + [t]
    res = 0
    #ans
    for i in range(n-1):
        res += (count[i] * k[i]) % mod
    print(res % mod)
