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);
  int T;
  cin >> T;
  while (T--) {
    int n, m, k;
    cin >> n >> m >> k;
    vector<vector<int>> G(n + 1);
    for (int i = 1; i <= m; i++) {
      int u, v;
      cin >> u >> v;
      G[u].push_back(v);
      G[v].push_back(u);
    }
    if (k == 1) {
      cout << "2\n";
      cout << "1\n";
      continue;
    }
    vector<int> deg(n + 1);
    vector<int> bad(n + 1);
    queue<int> Q;
    for (int i = 1; i <= n; i++) {
      sort(G[i].begin(), G[i].end());
      deg[i] = (int)G[i].size();
      if (deg[i] < k - 1) {
        Q.push(i);
        bad[i] = 1;
      }
    }
    while (!Q.empty()) {
      int cur = Q.front();
      assert(bad[cur] == 1);
      Q.pop();
      for (auto nx : G[cur]) {
        deg[nx] -= 1;
        if (!bad[nx] && deg[nx] < k - 1) {
          assert(deg[nx] == k - 2);
          Q.push(nx);
          bad[nx] = 1;
        }
      }
    }
    auto check = [&](const vector<int>& nodes) -> bool {
      for (auto v1 : nodes) {
        for (auto v2 : nodes) {
          if (v1 == v2) {
            continue;
          }
          auto it = lower_bound(G[v1].begin(), G[v1].end(), v2);
          if (it == G[v1].end()) {
            return false;
          }
          if (*it != v2) {
            return false;
          }
        }
      }
      return true;
    };
    auto find_clique = [&]() -> bool {
      for (int i = 1; i <= n; i++) {
        if (deg[i] == k - 1) {
          assert(bad[i] == 0);
          Q.push(i);
        }
      }
      while (!Q.empty()) {
        int cur = Q.front();
        Q.pop();
        assert(bad[cur] == 0);
        bad[cur] = 1;
        if (deg[cur] == k - 1) {
          vector<int> nodes;
          nodes.push_back(cur);
          for (auto nx : G[cur]) {
            if (bad[nx]) {
              continue;
            }
            nodes.push_back(nx);
          }
          assert(nodes.size() == k);
          if (check(nodes)) {
            cout << "2\n";
            for (auto v : nodes) {
              cout << v << " ";
            }
            cout << "\n";
            return true;
          }
        }
        for (auto nx : G[cur]) {
          deg[nx] -= 1;
          if (deg[nx] == k - 1) {
            Q.push(nx);
          }
        }
      }
      return false;
    };
    if (find_clique()) {
      continue;
    }
    vector<int> ans;
    for (int i = 1; i <= n; i++) {
      if (!bad[i]) {
        ans.push_back(i);
      }
    }
    if (ans.empty()) {
      cout << "-1\n";
    } else {
      cout << "1 " << ans.size() << "\n";
      for (auto v : ans) {
        cout << v << " ";
      }
      cout << "\n";
    }
  ddd:;
  }
  return 0;
}