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;
void setIO() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  cout.tie(nullptr);
}
const int MAX = 2e5 + 5;
const int LEN = 1e6 + 5;
const int LVL = 2e1 + 0;
const long long int MOD = 1e9 + 7;
const long long int INF = 9e9;
int xyz = 1;
int n, m, k;
int deg[MAX];
int vst[MAX];
vector<int> con[MAX];
queue<int> que;
void add(int i) { vst[i] = 1, que.push(i); }
bool clq(int p) {
  vector<int> cur(1, p);
  for (int adj : con[p]) {
    if (vst[adj] == 2) continue;
    if (deg[adj] <= k - 2) return false;
    cur.push_back(adj);
  }
  for (int i : cur) {
    for (int j : cur) {
      if (i == j) break;
      if (!binary_search(con[i].begin(), con[i].end(), j)) return false;
    }
  }
  cout << "2\n";
  for (int ele : cur) cout << ele << " ";
  cout << endl;
  return true;
}
void run() {
  cin >> n >> m >> k;
  while (!que.empty()) que.pop();
  for (int i = 1; i <= n; i++) con[i].clear(), deg[i] = vst[i] = 0;
  for (int i = 1; i <= m; i++) {
    int u;
    int v;
    cin >> u >> v;
    con[u].push_back(v);
    con[v].push_back(u);
    deg[u]++;
    deg[v]++;
  }
  for (int i = 1; i <= n; i++) sort(begin(con[i]), end(con[i]));
  if (k >= 500) {
    cout << "-1\n";
    return;
  }
  for (int i = 1; i <= n; i++)
    if (deg[i] < k) add(i);
  while (!que.empty()) {
    int pos = que.front();
    que.pop();
    vst[pos] = 2;
    if (deg[pos] == k - 1)
      if (clq(pos)) return;
    for (int adj : con[pos]) {
      if (--deg[adj] < k && !vst[adj]) add(adj);
    }
  }
  for (int i = 1; i <= n; i++) {
    if (!vst[i]) {
      vector<int> ans;
      for (int j = 1; j <= n; j++)
        if (!vst[j]) ans.push_back(j);
      cout << 1 << " " << ans.size() << "\n";
      for (int ele : ans) cout << ele << " ";
      cout << endl;
      return;
    }
  }
  cout << "-1" << endl;
}
int main() {
  setIO();
  cin >> xyz;
  while (xyz--) run();
  return 0;
}