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 max_n = 150;
int main() {
  int t, n, m, k, u, v;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d%d", &n, &m, &k);
    vector<vector<int> > g(n + 1);
    vector<int> du(n + 1);
    for (int i = 0; i < m; ++i) {
      scanf("%d%d", &u, &v);
      g[u].push_back(v);
      g[v].push_back(u);
    }
    queue<int> q;
    vector<int> vis(n + 1);
    for (int i = 1; i <= n; ++i) {
      sort(g[i].begin(), g[i].end());
      du[i] = g[i].size();
      if (du[i] < k) {
        vis[i] = 1;
        q.push(i);
      }
    }
    vector<int> ans;
    bool f = 0;
    while (!q.empty()) {
      u = q.front();
      q.pop();
      vis[u] = 2;
      if (du[u] == k - 1 && ans.empty() && k * (k - 1) / 2 <= m &&
          1ll * k * (k - 1) / 2 <= m) {
        ans.push_back(u);
        for (auto i : g[u]) {
          if (vis[i] < 2) {
            ans.push_back(i);
          }
        }
        f = 1;
        for (auto i : ans) {
          if (!f) {
            break;
          }
          for (auto j : ans) {
            if (i == j) {
              continue;
            }
            if (!binary_search(g[i].begin(), g[i].end(), j)) {
              f = 0;
              break;
            }
          }
        }
        if (!f) {
          ans.clear();
        }
      }
      if (f) {
        break;
      }
      for (auto i : g[u]) {
        if (--du[i] < k && !vis[i]) {
          vis[i] = 1;
          q.push(i);
        }
      }
    }
    if (f) {
      cout << 2 << endl;
      for (auto i : ans) {
        cout << i << " ";
      }
      cout << endl;
      continue;
    }
    int sum = 0;
    for (int i = 1; i <= n; ++i) {
      if (vis[i] == 0) {
        sum++;
      }
    }
    if (sum) {
      cout << 1 << " " << sum << endl;
      for (int i = 1; i <= n; ++i) {
        if (!vis[i]) {
          cout << i << " ";
        }
      }
      cout << endl;
      continue;
    }
    cout << -1 << endl;
  }
  return 0;
}