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);
    vector<int> deg(n + 1);
    for (int i = 1; i <= m; i++) {
      int x, y;
      cin >> x >> y;
      G[x].push_back(y);
      G[y].push_back(x);
      deg[x] += 1;
      deg[y] += 1;
    }
    for (int i = 1; i <= n; i++) {
      sort(G[i].begin(), G[i].end());
    }
    auto del = [&](int x, int y) -> void {
      deg[x] -= 1;
      deg[y] -= 1;
    };
    queue<int> Q;
    for (int i = 1; i <= n; i++) {
      if (deg[i] < k - 1) {
        Q.push(i);
      }
    }
    while (!Q.empty()) {
      int cur = Q.front();
      Q.pop();
      for (auto nx : G[cur]) {
        if (deg[nx] == 0) {
          continue;
        }
        del(cur, nx);
        if (deg[nx] == k - 2) {
          Q.push(nx);
        }
      }
      assert(deg[cur] == 0);
    }
    auto go = [&]() -> void {
      for (int i = 1; i <= n; i++) {
        if (deg[i] == k - 1) {
          Q.push(i);
        }
      }
      while (!Q.empty()) {
        int cur = Q.front();
        Q.pop();
        if (deg[cur] == k - 1) {
          bool good = true;
          vector<int> vec;
          for (auto nx : G[cur]) {
            if (deg[nx]) {
              vec.push_back(nx);
            }
          }
          assert(vec.size() == k - 1);
          for (int i = 0; good && i < k - 1; i++) {
            for (int j = i + 1; good && j < k - 1; j++) {
              int x = vec[i];
              int y = vec[j];
              auto it = lower_bound(G[x].begin(), G[x].end(), y);
              if (it == G[x].end() || *it != y) {
                good = false;
              }
            }
          }
          if (good) {
            cout << "2\n";
            for (auto t : vec) {
              cout << t << " ";
            }
            cout << cur << "\n";
            return;
          }
        }
        for (auto nx : G[cur]) {
          if (deg[nx] == 0) {
            continue;
          }
          del(cur, nx);
          if (deg[nx] == k - 1) {
            Q.push(nx);
          }
        }
      }
      vector<int> ans;
      for (int i = 1; i <= n; i++) {
        if (deg[i]) {
          ans.push_back(i);
        }
      }
      if (ans.empty()) {
        cout << -1 << "\n";
      } else {
        cout << "1 " << ans.size() << "\n";
        for (auto t : ans) {
          cout << t << " ";
        }
        cout << "\n";
      }
    };
    go();
  }
  return 0;
}