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

# sys.setrecursionlimit(300000)
t = int(input())

from types import GeneratorType
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=1000000007
for _ in range(t):
    class Graph:

        def __init__(self, V):
            self.V = V
            self.adj = [[] for i in range(V)]
        @bootstrap
        def DFSUtil(self, v):
            total = 1
            visited[v] = True

            for i in self.adj[v]:
                if visited[i] == False:
                    count = yield self.DFSUtil(i)
                    weights.append(count * (n - count))
                    total += count
            yield total

        def addEdge(self, v, w):
            self.adj[v].append(w)
            self.adj[w].append(v)



    weights = []
    n = int(input())
    G = Graph(n)
    for _ in range(n - 1):
        u, v = list(map(lambda x: int(x), input().split()))
        G.addEdge(u - 1, v - 1)
    visited = [False for _ in range(n)]

    G.DFSUtil(0)

    k = int(input())
    a = list(map(lambda x: int(x), input().split()))
    a.sort()
    leaf = 0
    for i in G.adj:
        if len(i) == 1:
            leaf += 1
    non_leaf = n - 1 - leaf

    if k < n - 1:
        a = [1] * (n - k - 1) + a

    if k > n - 1:
        ans = 1
        for i in range(n - 2,k):
            ans = (ans%mod * a[i]%mod)%mod
        a[n - 2] = ans
        # ,

    # print(a)


    ans = 0
    # print(non_leaf,leaf,"nasdsada")
    weights.sort()

    for i in range(0, n-1):
        ans =(ans+ (weights[i]%mod * a[i]%mod)%mod)%mod
    print(ans)