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;
using ll = long long;
template <class A, class B>
ostream& operator<<(ostream& os, const pair<A, B>& p) {
  return os << '(' << p.first << ", " << p.second << ')';
}
template <class T>
auto operator<<(ostream& os, T&& x) -> decltype(x.begin(), os) {
  os << '{';
  for (auto it = x.begin(); it != x.end(); ++it)
    os << *it << (it == prev(x.end()) ? "" : ", ");
  return os << '}';
}
void dump() {}
template <class T, class... Args>
void dump(T&& x, Args... args) {
  cerr << x << ";  ";
  dump(args...);
}
int t, n, m, k;
vector<bool> active;
vector<int> sz, ans;
vector<vector<int>> edge;
bool clique;
void rem(int x) {
  if (!active[x] || clique) return;
  active[x] = false;
  vector<int> candidates;
  int total_sz = sz[x];
  for (int i : edge[x]) {
    if (active[i]) {
      candidates.push_back(i);
      total_sz += sz[i];
    }
  }
  if ((int)candidates.size() == k - 1 && k * (k - 1) <= total_sz) {
    bool found = true;
    for (int i = 0; i < (int)candidates.size() && found; ++i) {
      for (int j = i + 1; j < (int)candidates.size() && found; ++j) {
        if (!binary_search((edge[candidates[i]]).begin(),
                           (edge[candidates[i]]).end(), candidates[j])) {
          found = false;
        }
      }
    }
    if (found) {
      clique = true;
      ans = candidates;
      ans.push_back(x);
      return;
    }
  }
  for (int i = 0; i < (int)edge[x].size(); ++i) {
    if (active[edge[x][i]]) {
      --sz[edge[x][i]];
      if (sz[edge[x][i]] < k) {
        rem(edge[x][i]);
      }
    }
  }
}
void solve() {
  cin >> n >> m >> k;
  clique = false;
  ans.clear();
  active.clear();
  active.resize(n, 1);
  sz.clear();
  sz.resize(n, 0);
  edge.clear();
  edge.resize(n);
  for (int i = 0, x, y; i < m; ++i) {
    cin >> x >> y;
    --x, --y;
    sz[x]++, sz[y]++;
    edge[x].push_back(y);
    edge[y].push_back(x);
  }
  for (int i = 0; i < n; ++i) sort((edge[i]).begin(), (edge[i]).end());
  for (int i = 0; i < n; ++i) {
    if (sz[i] < k) {
      if (active[i]) rem(i);
      if (clique) {
        cout << "2\n";
        for (int j : ans) cout << j + 1 << " ";
        cout << "\n";
        return;
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    if (active[i]) {
      ans.push_back(i);
    }
  }
  if ((int)ans.size() > k) {
    cout << "1 " << ans.size() << "\n";
    for (int i : ans) cout << i + 1 << " ";
    cout << "\n";
  } else {
    cout << "-1\n";
  }
}
int main() {
  ios::sync_with_stdio(false);
  for (cin >> t; t--;) solve();
  return 0;
}