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 sys import stdin


def inp():
    return stdin.buffer.readline().rstrip().decode('utf8')


def itg():
    return int(stdin.buffer.readline())


def mpint():
    return map(int, stdin.buffer.readline().split())


# ############################## import
from copy import deepcopy
from itertools import chain


def to_1d(iterable):
    """ 2d iterable to 1d """
    return list(chain(*iterable))


def to_tree(graph, root=0):
    """
    graph: undirected graph (adjacency list)
    :return directed graph that parent -> children
    """
    graph[:] = map(set, graph)

    stack = [[root]]
    while stack:
        if not stack[-1]:
            del stack[-1]
            continue
        vertex = stack[-1].pop()
        for e in graph[vertex]:
            graph[e].remove(vertex)
        stack.append(list(graph[vertex]))

    graph[:] = map(list, graph)


def to_graph(tree, to_list=False):
    """ :return undirected graph (adjacency list) """
    tree[:] = map(set, tree)
    for node1, node_set in enumerate(deepcopy(tree)):
        for node2 in node_set:
            tree[node2].add(node1)
    if to_list:
        tree[:] = map(list, tree)


def tree_bfs(tree, start=0, flat=False) -> list:
    stack = [start]
    result = []
    while stack:
        new_stack = []
        if flat:
            result.extend(stack)
        else:
            result.append(stack)
        for node in stack:
            new_stack.extend(tree[node])
        stack = new_stack
    return result


def tree_postorder(tree, root=0, flat=False):
    return tree_bfs(tree, root, flat=flat)[::-1]


def tree_edge_descendant(tree, edge_time_count=False, root=0):
    """
    :return: a list for the number of vertices under each edge

    if edge_time_count:
    :return a list for the sum of times that walking on each edge
    the walk mean the path of any pair (u, v) and (u < v)
    """
    vertices = len(tree)
    graph = deepcopy(tree)
    to_graph(graph)
    results = [[] for _ in range(vertices)]
    for leaves in tree_postorder(tree)[:-1]:
        for leaf in leaves:
            graph[leaf] = list(graph[leaf])
            graph[graph[leaf][0]].remove(leaf)
        for leaf in leaves:
            children = sum(results[leaf]) + 1
            results[graph[leaf][0]].append(children)

    if edge_time_count:
        for result in results:
            result[:] = map(lambda x: x * (vertices - x), result)
    return results


# ############################## main
from functools import reduce

MOD = int(1e9) + 7
g = []

for __ in range(itg()):
    n = itg()
    g = [list() for _ in range(n)]
    for _ in range(n - 1):
        u, v = mpint()
        g[u - 1].append(v - 1)
        g[v - 1].append(u - 1)
    to_tree(g)
    m = itg()
    factors = sorted(mpint())
    count = tree_edge_descendant(g, True)
    n -= 1
    if n >= m:
        factors = ([1] * (n - m)) + factors
    else:  # n < m
        while len(factors) != n:
            factors[-1] = factors[-2] * factors.pop() % MOD
    count = sorted(to_1d(count))
    # print(count)
    print(
        reduce(
            lambda a, b: (a + b) % MOD,
            (time * value % MOD for time, value in zip(count, factors)),
            0
        )
    )
# Please check!
