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 MAXN = 100010;
unordered_set<int> x[MAXN];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int times;
  cin >> times;
  while (times--) {
    int n, m, k;
    cin >> n >> m >> k;
    for (int i = 1; i <= n; ++i) {
      x[i].clear();
    }
    for (int i = 0; i < m; ++i) {
      int a, b;
      cin >> a >> b;
      x[a].insert(b);
      x[b].insert(a);
    }
    queue<int> q;
    for (int i = 1; i <= n; ++i) {
      if (x[i].size() >= k - 1) continue;
      q.push(i);
    }
    while (!q.empty()) {
      int a = q.front();
      q.pop();
      for (int b : x[a]) {
        x[b].erase(a);
        if (x[b].size() >= k - 1) continue;
        q.push(b);
      }
      x[a].clear();
    }
    auto check_clique = [&](int a) -> bool {
      if (x[a].size() != k - 1) return false;
      unordered_set<int> s = x[a];
      s.insert(a);
      for (int b : x[a]) {
        int cnt = 0;
        for (int c : s) {
          if (x[b].find(c) != x[b].end()) ++cnt;
        }
        if (cnt != k - 1) return false;
      }
      return true;
    };
    for (int i = 1; i <= n; ++i) {
      if (x[i].size() == k - 1) q.push(i);
    }
    vector<int> clique;
    while (!q.empty()) {
      int a = q.front();
      q.pop();
      if (check_clique(a)) {
        clique.push_back(a);
        for (int b : x[a]) clique.push_back(b);
        break;
      } else {
        for (int b : x[a]) {
          x[b].erase(a);
          if (x[b].size() > k - 1) continue;
          q.push(b);
        }
        x[a].clear();
      }
    }
    if (clique.size() > 0) {
      cout << 2 << endl;
      for (int a : clique) cout << a << " ";
      cout << endl;
      continue;
    }
    vector<int> ans;
    for (int i = 1; i <= n; ++i) {
      if (x[i].size() > 0) ans.push_back(i);
    }
    if (ans.size() > 0) {
      cout << "1 " << ans.size() << endl;
      for (int a : ans) cout << a << " ";
      cout << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}