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 sys
from collections import deque
input = sys.stdin.readline
for _ in range(int(input())):
    level = {}
    n = int(input())
    tree = {}
    edges = []
    for i in range(n-1):
        a, b = map(int, input().split())
        if a not in tree:
            tree[a] = []
        if b not in tree:
            tree[b] = []
        tree[a].append(b)
        tree[b].append(a)
        edges.append((a, b))
    m = int(input())
    p = list(map(int, input().split()))
    while len(p)<n-1:
        p.append(1) 
    stack = deque([1])
    seen = {}
    while stack:
        current = stack[0]
        if len(tree[current]) == 1 and current != 1:
            level[current] = 1
            stack.popleft()            
        else:
            if current in seen:
                for child in tree[current]:
                    if child in level:
                        level[current] = level.get(current, 1)+level[child]                
                stack.popleft()
            else:
                for nxt in tree[current]:
                    if nxt not in seen:
                        stack.appendleft(nxt)
        seen[current] = 1    
    frqs = []
    for edge in edges:
        a = edge[0]
        b = edge[1]
        if level[b]<level[a]:
            a,b = b,a
        frqs.append(level[a]*(n-level[a]))
    frqs.sort()
    p.sort()
    while(len(p)>n-1):
        p[n-2]*=p.pop()
        p[n-2] = p[n-2]%1000000007
    pr = 0
    for i in range(n-1):
        pr+=frqs[i]*p[i]
        pr = pr%1000000007
    print(pr)
    