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<vector<long long int> > v;
vector<long long int> s, a;
long long int n;
long long int dfs1(long long int u, long long int par) {
  s[u] = 1;
  for (auto it : v[u]) {
    if (it != par) {
      s[u] += dfs1(it, u);
      a.push_back(s[it] * 1ll * (n - s[it]));
    }
  }
  return s[u];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t = 1;
  cin >> t;
  while (t--) {
    long long int m, i, j, x, y, ans = 0;
    cin >> n;
    v.clear();
    s.clear();
    a.clear();
    v.resize(n + 1);
    s.resize(n + 1);
    a.clear();
    for (i = 1; i < n; i++) {
      cin >> x >> y;
      v[x].push_back(y);
      v[y].push_back(x);
    }
    cin >> m;
    vector<long long int> p(m);
    for (i = 0; i < m; i++) cin >> p[i];
    sort(p.begin(), p.end(), greater<long long int>());
    vector<long long int> q;
    i = 1;
    if (m > (n - 1)) {
      while (i <= (m - (n - 1))) {
        p[i] = (p[i] * p[i - 1]) % 1000000007;
        i++;
      }
    }
    i--;
    while (i < m) {
      q.push_back(p[i]);
      i++;
    }
    while (q.size() < (n - 1)) q.push_back(1);
    dfs1(1, -1);
    sort(a.begin(), a.end(), greater<long long int>());
    for (i = 0; i < (n - 1); i++)
      ans = (ans + (a[i] * 1ll * q[i]) % 1000000007) % 1000000007;
    cout << ans << "\n";
  }
  return 0;
}
