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.buffer.readline
mod = 10**9+7

def main():
    t = int(input())

    for _ in range(t):
        n = int(input())
        g = [[] for _ in range(n)]
        for i in range(n-1):
            u, v = map(int, input().split())
            u, v = u-1, v-1
            g[u].append(v)
            g[v].append(u)
        m = int(input())
        P = list(map(int, input().split()))
        P.sort()

        s = []
        visit = [-1]*n
        s.append(0)
        order = []
        par = [-1]*n
        while s:
            v = s.pop()
            order.append(v)
            for u in g[v]:
                if u == par[v]:
                    continue
                par[u] = v
                s.append(u)

        ans = 0
        c = [1]*n
        order.reverse()
        U = []
        for v in order:
            if par[v] != -1:
                cnt = (n-c[v])*c[v]
                U.append(cnt)
                c[par[v]] += c[v]
        #print(U)
        if len(U) >= len(P):
            U.sort(reverse=True)
            ans = 0
            for u in U:
                if P:
                    p = P.pop()
                else:
                    p = 1
                ans += u*p
                ans %= mod
        else:
            U.sort()
            P.sort()
            Q = P[0:len(U)]
            R = P[len(U):]
            for r in R:
                Q[-1] *= r
                Q[-1] %= mod
            for u, q in zip(U, Q):
                ans += u*q
                ans %= mod
        print(ans)

if __name__ == '__main__':
    main()
