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;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long INF = 1e18 + 123;
const long double EPS = 1e-9;
const int inf = 1e9 + 123;
const int MOD = 1e9 + 7;
const int N = 1e5 + 123;
const int M = 1e6 + 123;
const double pi = 3.14159265359;
const int dx[] = {0, 0, 1, -1};
const int dy[] = {1, -1, 0, 0};
int d[N];
bool del[N];
vector<int> g[N];
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 1; i <= n; i++) {
    g[i].clear();
    del[i] = 0;
  }
  for (int i = 1, u, v; i <= m; i++) {
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  set<pair<int, int> > s;
  for (int i = 1; i <= n; i++) {
    d[i] = (int)g[i].size();
    s.insert({d[i], i});
    sort(g[i].begin(), g[i].end());
  }
  while (!s.empty() && s.begin()->first < k) {
    int v = s.begin()->second;
    del[v] = 1;
    s.erase(s.begin());
    if (d[v] == k - 1) {
      vector<int> first;
      for (int u : g[v]) {
        if (!del[u]) {
          first.push_back(u);
        }
      }
      bool ok = 1;
      for (int i = 0; i < (int)first.size(); i++) {
        for (int j = 0; j < i; j++) {
          if (!binary_search(g[first[i]].begin(), g[first[i]].end(),
                             first[j])) {
            ok = 0;
            break;
          }
        }
      }
      if (ok) {
        cout << 2 << endl;
        for (int u : first) cout << u << " ";
        cout << v;
        return;
      }
    }
    for (int u : g[v]) {
      if (!del[u]) {
        s.erase({d[u], u});
        d[u]--;
        s.insert({d[u], u});
      }
    }
  }
  if (!s.empty()) {
    cout << 1 << " " << (int)s.size() << '\n';
    for (auto p : s) {
      cout << p.second << " ";
    }
    return;
  }
  cout << -1;
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int t = 1;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    solve();
    cout << '\n';
  }
  return 0;
}