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>
#pragma GCC optimize("Ofast")
using namespace std;
long long int gcd(long long int a, long long int b) {
  if (!b)
    return a;
  else
    return gcd(b, a % b);
}
const int MAXN = 111111;
vector<unordered_set<int>> adj(MAXN);
vector<int> deg(MAXN);
vector<bool> ded(MAXN);
set<pair<int, int>> s;
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  s.clear();
  for (int i = 1; i <= n; i++) {
    adj[i].clear();
    ded[i] = 0;
    deg[i] = 0;
  }
  for (int i = 0; i < m; i++) {
    int v, u;
    cin >> v >> u;
    adj[v].insert(u);
    adj[u].insert(v);
    deg[v]++;
    deg[u]++;
  }
  for (int i = 1; i <= n; i++) s.insert({deg[i], i});
  while (!s.empty()) {
    pair<int, int> v = *s.begin();
    s.erase(s.begin());
    if (v.first >= k) {
      cout << 1 << " " << (int)(s.size()) + 1 << '\n' << v.second << " ";
      for (auto x : s) cout << x.second << " ";
      cout << '\n';
      return;
    }
    if (v.first == k - 1 && (k * (k - 1)) / 2 <= m) {
      vector<int> can = {v.second};
      for (int x : adj[v.second]) {
        if (!ded[x]) can.push_back(x);
      }
      bool ok = 1;
      for (int i = 0; i < k; i++) {
        for (int j = i + 1; j < k; j++) {
          if (adj[can[i]].find(can[j]) == adj[can[i]].end()) {
            ok = 0;
            break;
          }
        }
        if (!ok) break;
      }
      if (ok) {
        cout << 2 << '\n';
        for (int x : can) cout << x << " ";
        cout << '\n';
        return;
      }
    }
    for (int x : adj[v.second]) {
      if (!ded[x] && s.find({deg[x], x}) != s.end()) {
        s.erase({deg[x], x});
        deg[x]--;
        s.insert({deg[x], x});
      }
    }
    ded[v.second] = 1;
  }
  cout << -1 << '\n';
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int t;
  cin >> t;
  srand(chrono::high_resolution_clock::now().time_since_epoch().count());
  while (t--) solve();
}