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.
#include <bits/stdc++.h>
using namespace std;
vector<long long> adj[100001];
long long vis[100001], n;
long long child[100001];
vector<long long> vect;
void dfs(long long x, long long p) {
  vis[x] = 1;
  child[x] = 1;
  for (long long y : adj[x]) {
    if (y == p) continue;
    dfs(y, x);
    child[x] += child[y];
    vect.push_back(child[y] * (n - child[y]));
  }
}
int main() {
  long long t;
  cin >> t;
  while (t--) {
    long long x, y;
    cin >> n;
    for (long long i = 1; i <= n; i++) {
      adj[i].clear();
    }
    adj[n].clear();
    memset(vis, 0, sizeof(vis));
    memset(child, 0, sizeof(vis));
    vect.clear();
    for (long long i = 1; i < n; i++) {
      cin >> x >> y;
      adj[x].push_back(y);
      adj[y].push_back(x);
    }
    dfs(1, 0);
    sort(vect.begin(), vect.end(), greater<long long>());
    long long m;
    cin >> m;
    long long p[m];
    for (long long i = 0; i < m; i++) {
      cin >> p[i];
    }
    sort(p, p + m, greater<long long>());
    long long ans = 0;
    if (m >= n - 1) {
      int i, j;
      for (i = m - 1, j = n - 2; j > 0; j--, i--) {
        ans = (ans % 1000000007 +
               (p[i] % 1000000007 * vect[j] % 1000000007) % 1000000007) %
              1000000007;
      }
      long long temp = 1;
      for (int k = i; k >= 0; k--) {
        temp = (temp % 1000000007 * p[k] % 1000000007) % 1000000007;
      }
      ans = (ans % 1000000007 +
             (temp % 1000000007 * vect[0] % 1000000007) % 1000000007) %
            1000000007;
    } else {
      for (int i = 0; i < n - 1; i++) {
        if (i < m)
          ans = (ans % 1000000007 +
                 (p[i] % 1000000007 * vect[i] % 1000000007) % 1000000007) %
                1000000007;
        else
          ans = (ans % 1000000007 + vect[i] % 1000000007) % 1000000007;
      }
    }
    ans %= 1000000007;
    cout << ans << endl;
  }
  return 0;
}
