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

from collections import Counter, defaultdict, deque

from types import GeneratorType

# From https://github.com/cheran-senthil/PyRival/blob/master/pyrival/misc/bootstrap.py
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to

    return wrappedfunc


MOD = 10 ** 9 + 7


def solve(N, edges, M, P):
    P.sort()
    if len(P) > N - 1:
        edgeVals = P[: N - 1]
        last = 1
        for i in range(N - 1, len(P)):
            last = (last * P[i]) % MOD
        edgeVals[-1] = (edgeVals[-1] * last) % MOD
    else:
        edgeVals = ([1] * ((N - 1) - len(P))) + P
    assert len(edgeVals) == N - 1

    graph = [[] for i in range(N)]
    for u, v in edges:
        graph[u].append(v)
        graph[v].append(u)

    size = [0 for i in range(N)]

    @bootstrap
    def dfs(node, p):
        total = 1
        for child in graph[node]:
            if child != p:
                yield dfs(child, node)
                total += size[child]
        size[node] = total
        yield

    dfs(0, -1)
    edges2 = []
    for i, (u, v) in enumerate(edges):
        left = min(size[u], size[v])
        right = N - left
        edges2.append(left * right)
    edges2.sort()

    ans = 0
    for count, vals in zip(edges2, edgeVals):
        ans += count * vals
        ans %= MOD
    return ans % MOD


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    TC = int(input())
    for tc in range(1, TC + 1):
        (N,) = [int(x) for x in input().split()]

        edges = [
            [int(x) - 1 for x in input().split()] for i in range(N - 1)
        ]  # 0 indexed
        (M,) = [int(x) for x in input().split()]
        P = [int(x) for x in input().split()]
        ans = solve(N, edges, M, P)
        print(ans)
