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;
template <class T>
struct segment_tree {
  int n;
  vector<T> v;
  vector<int> t;
  segment_tree();
  segment_tree(int n_, T mx) : n(n_), v(n, mx), t(2 * n) {
    for (int i = 2 * n - 1; i >= n; i--) {
      t[i] = i - n;
    }
    for (int i = n - 1; i >= 0; i--) {
      t[i] = t[2 * i];
    }
  }
  void update(int i, T x) {
    v[i] = x;
    i += n;
    while (i > 1) {
      i /= 2;
      t[i] = v[t[2 * i]] < v[t[2 * i + 1]] ? t[2 * i] : t[2 * i + 1];
    }
  }
};
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<unordered_set<int>> graph(n);
  for (int i = 0; i < (int)(m); i++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    graph[u].insert(v);
    graph[v].insert(u);
  }
  segment_tree<int> deg(n, 1e9);
  for (int i = 0; i < (int)(n); i++) deg.update(i, graph[i].size());
  set<int> left;
  for (int i = 0; i < (int)(n); i++) left.insert(i);
  while (deg.v[deg.t[1]] < k) {
    int a = deg.t[1];
    deg.update(a, 1e9);
    left.erase(a);
    if ((int)graph[a].size() == k - 1) {
      bool ok = true;
      for (int b : graph[a]) {
        for (int c : graph[a]) {
          if (b != c && !graph[b].count(c)) {
            ok = false;
            break;
          }
        }
        if (!ok) break;
      }
      if (ok) {
        cout << 2 << endl;
        for (int b : graph[a]) cout << b + 1 << " ";
        cout << a + 1 << endl;
        return;
      }
    }
    for (int b : graph[a]) {
      graph[b].erase(a);
      deg.update(b, graph[b].size());
    }
    graph[a].clear();
  }
  if (left.empty()) {
    cout << -1 << endl;
    return;
  }
  cout << 1 << " " << left.size() << endl;
  for (int u : left) cout << u + 1 << " ";
  cout << endl;
}
void cleanup() {}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  for (int test = 0; test < (int)(t); test++) {
    solve();
    cleanup();
  }
  return 0;
}