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;
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<int> adj[n];
  unordered_map<int, int> mapas[n];
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
    mapas[u][v] = 1;
    mapas[v][u] = 1;
  }
  if (k > 500) {
    cout << "-1\n";
    return;
  }
  bool removed[n];
  int leftEdges[n];
  queue<int> eile;
  for (int i = 0; i < n; i++) {
    if (adj[i].size() <= k - 1) eile.push(i);
    leftEdges[i] = adj[i].size();
    removed[i] = false;
  }
  while (!eile.empty()) {
    int g = eile.front();
    eile.pop();
    if (removed[g]) continue;
    for (int i = 0; i < adj[g].size(); i++) {
      if (removed[adj[g][i]]) {
        swap(adj[g][i], adj[g].back());
        adj[g].pop_back();
        i--;
      }
    }
    if (leftEdges[g] == k - 1) {
      vector<int> clique;
      for (int i = 0; i < adj[g].size(); i++) clique.push_back(adj[g][i]);
      bool galima = true;
      for (int i = 0; i < clique.size(); i++) {
        for (int j = i + 1; j < clique.size(); j++) {
          if (!mapas[clique[i]][clique[j]]) galima = false;
        }
      }
      if (galima) {
        cout << "2\n";
        cout << g + 1 << " ";
        for (int i = 0; i < clique.size(); i++) cout << clique[i] + 1 << " ";
        cout << "\n";
        return;
      }
    }
    for (int i = 0; i < adj[g].size(); i++) {
      int next = adj[g][i];
      leftEdges[next]--;
      if (leftEdges[next] <= k - 1) eile.push(next);
    }
    removed[g] = true;
  }
  vector<int> left;
  for (int i = 0; i < n; i++) {
    if (!removed[i]) {
      left.push_back(i);
    }
  }
  if (left.size() >= k + 1) {
    cout << "1 " << left.size() << "\n";
    for (int i = 0; i < left.size(); i++) cout << left[i] + 1 << " ";
    cout << "\n";
  } else
    cout << "-1\n";
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}