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")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<int>> g(n);
  vector<int> deg(n, 0);
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    g[x].push_back(y);
    g[y].push_back(x);
    deg[x]++;
    deg[y]++;
  }
  vector<bool> done(n, false);
  vector<int> vec;
  vector<vector<int>> adj(n), check(n);
  for (int i = 0; i < n; i++) {
    if (deg[i] < k) vec.push_back(i);
  }
  while (vec.size()) {
    int s = vec.back();
    vec.pop_back();
    done[s] = true;
    if (deg[s] == k - 1) {
      for (int t : g[s]) {
        if (done[t]) continue;
        adj[s].push_back(t);
        check[t].push_back(s);
      }
    }
    for (int t : g[s]) {
      deg[t]--;
      if (deg[t] == k - 1) vec.push_back(t);
    }
  }
  for (int i = 0; i < n; i++) {
    if (!done[i]) vec.push_back(i);
  }
  if (vec.size()) {
    printf("1 %d\n", vec.size());
    for (int i = 0; i < vec.size(); i++) {
      printf("%d ", vec[i] + 1);
    }
    printf("\n");
    return;
  }
  vector<bool> is_ok(n, true);
  vector<int> flag(n, 0);
  for (int i = 0; i < n; i++) {
    for (int v : g[i]) {
      flag[v] = 1;
    }
    flag[i] = 1;
    for (int v : check[i]) {
      for (int u : adj[v]) {
        if (!flag[u]) {
          is_ok[v] = false;
        }
      }
    }
    flag[i] = 0;
    for (int v : g[i]) {
      flag[v] = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    if (adj[i].size() != k - 1) continue;
    if (is_ok[i]) {
      printf("2\n");
      printf("%d", i + 1);
      for (int v : adj[i]) {
        printf(" %d", v + 1);
      }
      printf("\n");
      return;
    }
  }
  printf("-1\n");
  return;
}
int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int q;
  cin >> q;
  while (q--) {
    solve();
  }
}