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>
#pragma GCC optimize("O3")
using namespace std;
const int N = 1e6 + 7;
const int INF = 1e9 + 7;
const int T = (1 << 20);
int n, k;
int dfs(int start, int przodek, vector<vector<int> >& G,
        vector<long long>& kraw) {
  int roz = 1;
  for (auto& u : G[start]) {
    if (u == przodek) continue;
    int pom = dfs(u, start, G, kraw);
    kraw.push_back(1ll * pom * (n - pom));
    roz += pom;
  }
  return roz;
}
void solve() {
  cin >> n;
  vector<vector<int> > G(n);
  for (int i = 1; i < n; i++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  cin >> k;
  vector<long long> tab(k);
  for (auto& u : tab) cin >> u;
  sort(tab.begin(), tab.end());
  while ((int)tab.size() > n - 1) {
    tab[(int)tab.size() - 2] = tab[(int)tab.size() - 2] * tab.back() % INF;
    tab.pop_back();
  }
  reverse(tab.begin(), tab.end());
  while ((int)tab.size() < n - 1) tab.push_back(1);
  vector<long long> kraw;
  dfs(0, -1, G, kraw);
  sort(kraw.begin(), kraw.end());
  for (auto& u : kraw) u %= INF;
  reverse(kraw.begin(), kraw.end());
  long long ans = 0;
  for (int i = 0; i < n - 1; i++) ans = (ans + kraw[i] * tab[i]) % INF;
  cout << ans << '\n';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}
