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

# import math
from collections import deque

# import heapq

# from math import inf
# from math import gcd

# print(help(deque))
# 26
pprint = lambda s: print(' '.join(map(lambda x: str(x), s)))
input = lambda: sys.stdin.readline().strip()
ipnut = input
mod = 1000000007
for _ in range(int(input())):
    # z1, o1, t1 = map(int, input().split())
    n = int(input())
    g = [[] for i in range(n)]
    for i in range(n - 1):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        g[a].append(b)
        g[b].append(a)
    # a = list(map(int, input().split()))
    k = int(input())
    lol = list(sorted(map(int, input().split())))
    if k < n - 1:
        lol = [1] * (n - 1-k) + lol
    else:
        for i in range(k - n + 1):
            lol[-2] = (lol[-1] * lol[-2]) % mod
            del lol[-1]
    # print(lol)
    lvl = [-1 for i in range(n)]
    lvl[0] = 0
    bfs = deque()
    bfs.append(0)
    while bfs:
        v = bfs.popleft()
        for u in g[v]:
            if lvl[u] == -1:
                lvl[u] = lvl[v] + 1
                bfs.append(u)
    ver = [i for i in range(n)]
    ver.sort(key=lambda x: -lvl[x])
    # print(ver)
    under = [-1] * n
    ans = []
    for v in ver[:-1]:
        under[v] = 1
        for u in g[v]:
            if under[u] != -1:
                under[v] += under[u]
        ans.append((under[v] * (n - under[v])))
    # print(under)
    ans.sort()
    ansv = 0
    for i in range(n - 1):
        ansv = (ansv + (ans[-1 - i] * lol[-1 - i]) % mod) % mod
    print(ansv)

