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;input=sys.stdin.readline
T, = map(int, input().split())
for _ in range(T):
    N, = map(int, input().split())
    d = [set() for _ in range(N+1)]
    for i in range(N-1):
        u, v = map(int, input().split())
        d[u].add((v, i))
        d[v].add((u, i))

    G = [set() for _ in range(N+1)]
    stack = [2]
    vs = set([2])
    vs_dfs = list()
    while stack:
        v = stack.pop()
        vs_dfs.append(v)
        for u, i in d[v]:
            if u in vs:
                continue
            G[v].add((u, i))
            vs.add(u)
            stack.append(u)

    size = [0]*(N+1)
    X = [0]*(N-1)
    for v in vs_dfs[::-1]:
        tmp = 1
        for u, i in G[v]:
            tmp += size[u]
            X[i] = size[u]*(N-size[u])
        size[v] = tmp
    M, = map(int, input().split())
    P = list(map(int, input().split()))
    X.sort()
    X=X[::-1]
    mod = 10**9+7
    if N-1>=M:
        P.sort()
        P=P[::-1]
        for _ in range(N-1-M):
            P.append(1)
    else:
        P.sort()
        for _ in range(M-(N-1)):
            p = P.pop()
            P[-1] = P[-1]*p%mod
        P=P[::-1]
    R = 0
    for x, p in zip(X,P):
        R = (R+x*p)%mod
#    print(X, P)
    print(R)
