Problem: You are given an undirected graph with n vertices and m edges. Also, you are given an integer k.

Find either a clique of size k or a non-empty subset of vertices such that each vertex of this subset has at least k neighbors in the subset. If there are no such cliques and subsets report about it.

A subset of vertices is called a clique of size k if its size is k and there exists an edge between every two vertices from the subset. A vertex is called a neighbor of the other vertex if there exists an edge between them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The next lines contain descriptions of test cases.

The first line of the description of each test case contains three integers n, m, k (1 ≤ n, m, k ≤ 10^5, k ≤ n).

Each of the next m lines contains two integers u, v (1 ≤ u, v ≤ n, u ≠ v), denoting an edge between vertices u and v.

It is guaranteed that there are no self-loops or multiple edges. It is guaranteed that the sum of n for all test cases and the sum of m for all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case: 

If you found a subset of vertices such that each vertex of this subset has at least k neighbors in the subset in the first line output 1 and the size of the subset. On the second line output the vertices of the subset in any order.

If you found a clique of size k then in the first line output 2 and in the second line output the vertices of the clique in any order.

If there are no required subsets and cliques print -1.

If there exists multiple possible answers you can print any of them.

Example

Input


3
5 9 4
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
10 15 3
1 2
2 3
3 4
4 5
5 1
1 7
2 8
3 9
4 10
5 6
7 10
10 8
8 6
6 9
9 7
4 5 4
1 2
2 3
3 4
4 1
1 3


Output


2
4 1 2 3 
1 10
1 2 3 4 5 6 7 8 9 10 
-1

Note

In the first test case: the subset \{1, 2, 3, 4\} is a clique of size 4.

In the second test case: degree of each vertex in the original graph is at least 3. So the set of all vertices is a correct answer.

In the third test case: there are no cliques of size 4 or required subsets, so the answer is -1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int n, m, k;
    cin >> n >> m >> k;
    vector<vector<int> > edges(n + 1);
    unordered_map<int, int> mp[n + 1];
    int degree[n + 1];
    bool alive[n + 1];
    for (int i = 0; i < n + 1; i++) {
      degree[i] = 0, alive[i] = true;
    };
    for (int i = 0; i < m; i++) {
      int a, b;
      cin >> a >> b;
      edges[a].push_back(b);
      edges[b].push_back(a);
      mp[a][b] = 1;
      mp[b][a] = 1;
      degree[a]++;
      degree[b]++;
    }
    set<pair<int, int> > se;
    for (int i = 1; i < n + 1; i++) {
      se.insert({degree[i], i});
    }
    while (!se.empty()) {
      pair<int, int> p = *se.begin();
      int u = p.second;
      alive[u] = false;
      se.erase(se.begin());
      if (degree[u] >= k) {
        cout << 1 << " " << se.size() + 1 << '\n';
        cout << u << " ";
        for (auto x : se) {
          cout << x.second << " ";
        }
        cout << '\n';
        goto done;
      }
      if (degree[u] == k - 1) {
        vector<int> clique;
        clique.push_back(u);
        for (auto x : edges[u]) {
          if (alive[x]) clique.push_back(x);
        }
        bool pos = true;
        for (int i = 0; i < k; i++) {
          for (int j = i + 1; j < k; j++) {
            if (mp[clique[i]].find(clique[j]) == mp[clique[i]].end()) {
              pos = false;
              break;
            }
          }
        }
        if (pos) {
          cout << 2 << '\n';
          for (auto x : clique) {
            cout << x << " ";
          }
          cout << '\n';
          goto done;
        }
      }
      for (auto x : edges[u]) {
        degree[u]--;
        if (!alive[x]) continue;
        se.erase({degree[x], x});
        degree[x]--;
        se.insert({degree[x], x});
      }
    }
    cout << "-1" << '\n';
  done:
    bool dummy = true;
  }
  return 0;
}