D. Maximum Distributed Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 \sum\limits_{i=1}^{n-1} \sum\limits_{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.InputThe first line contains one integer t (1 \le t \le 100) — the number of test cases.The first line of each test case contains a single integer n (2 \le n \le 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 \le u_i, v_i \le n; u_i \ne v_i) — indices of vertices connected by the i-th edge.Next line contains a single integer m (1 \le m \le 6 \cdot 10^4) — the number of prime factors of k.Next line contains m prime numbers p_1, p_2, \ldots, p_m (2 \le p_i < 6 \cdot 10^4) such that k = p_1 \cdot p_2 \cdot \ldots \cdot 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 \cdot 10^4, and the given edges for each test cases form a tree.OutputPrint the maximum distribution index you can get. Since answer can be too large, print it modulo 10^9+7.ExampleInput
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:   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:   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.
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

17 18 286 
['dfs and similar', 'dp', 'greedy', 'implementation', 'math', 'number theory', 'sortings', 'trees', '*1800']