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;
const int N = 100000;
int eo[N], *ej[N], dd[N], qu[N];
bool removed[N];
void init(int n) {
  fill(eo, eo + n, 0);
  for (int i = 0; i < n; i++) ej[i] = (int *)malloc(2 * sizeof *ej[i]);
  fill(dd, dd + n, 0);
  fill(removed, removed + n, false);
}
void append(int i, int j) {
  int o = eo[i]++;
  dd[i]++;
  if (o >= 2 && (o & o - 1) == 0)
    ej[i] = (int *)realloc(ej[i], (o << 1) * sizeof *ej[i]);
  ej[i][o] = j;
}
struct Cmp {
  bool operator()(int i, int j) const {
    return dd[i] < dd[j] || dd[i] == dd[j] && i < j;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int n, m, k;
    cin >> n >> m >> k;
    int k_ = (long long)k * (k - 1) / 2 <= m ? k - 1 : k;
    init(n);
    unordered_set<long long> s;
    for (int h = 0; h < m; h++) {
      int i, j;
      cin >> i >> j, i--, j--;
      if (i > j) swap(i, j);
      s.insert((long long)i << 20 | j);
      append(i, j);
      append(j, i);
    }
    set<int, Cmp> pq;
    for (int i = 0; i < n; i++) pq.insert(i);
    bool found = false;
    while (!pq.empty()) {
      int i = *pq.begin();
      if (dd[i] >= k) {
        cout << "1 " << pq.size() << '\n';
        for (int j : pq) cout << j + 1 << ' ';
        cout << '\n';
        found = true;
        break;
      }
      if (dd[i] >= k_) {
        bool clique = true;
        int cnt = 0;
        qu[cnt++] = i;
        for (int o = eo[i]; o--;) {
          int j = ej[i][o];
          if (!removed[j]) qu[cnt++] = j;
        }
        for (int h1 = 1; h1 < cnt; h1++) {
          int u = qu[h1];
          for (int h2 = h1 + 1; h2 < cnt; h2++) {
            int v = qu[h2];
            if (s.find(u < v ? (long long)u << 20 | v
                             : (long long)v << 20 | u) == s.end()) {
              clique = false;
              goto out;
            }
          }
        }
      out:
        if (clique) {
          cout << "2\n";
          while (cnt--) cout << qu[cnt] + 1 << ' ';
          cout << '\n';
          found = true;
          break;
        }
      }
      pq.erase(i);
      removed[i] = true;
      for (int o = eo[i]; o--;) {
        int j = ej[i][o];
        if (!removed[j]) {
          pq.erase(j);
          dd[j]--;
          pq.insert(j);
        }
      }
    }
    if (!found) cout << "-1\n";
  }
  return 0;
}