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 solve() {
  int N, M, K;
  scanf("%d%d%d", &N, &M, &K);
  vector<vector<int>> con(N + 1);
  vector<int> deg(N + 1);
  for (int i = 1; i <= M; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    con[a].push_back(b);
    con[b].push_back(a);
    deg[a]++;
    deg[b]++;
  }
  if ((long long)K * (K - 1) > M + M) {
    puts("-1");
    return;
  }
  set<pair<int, int>> deg_set;
  for (int i = 1; i <= N; i++) deg_set.insert({deg[i], i});
  vector<int> order(N + 1), seq;
  while (!deg_set.empty()) {
    static int ocnt = 0;
    auto [d, u] = *deg_set.begin();
    order[u] = ++ocnt;
    seq.push_back(u);
    if (d >= K) {
      vector<int> grp;
      for (int i = 1; i <= N; i++)
        if (deg[i] != -1) grp.push_back(i);
      printf("1 %d\n", ((int)(grp).size()));
      for (int v : grp) printf("%d ", v);
      puts("");
      return;
    }
    deg_set.erase({d, u});
    deg[u] = -1;
    for (int v : con[u])
      if (deg[v] != -1) {
        deg_set.erase({deg[v], v});
        deg[v]--;
        deg_set.insert({deg[v], v});
      }
  }
  vector<vector<pair<int, int>>> check_list(N + 1);
  vector<int> color(N + 1);
  vector<bool> found(N + 1);
  for (int u : seq) {
    static int ccnt = 0;
    ccnt++;
    vector<int> arr;
    for (int v : con[u]) {
      if (order[u] < order[v]) arr.push_back(v);
      color[v] = ccnt;
    }
    for (auto [v, p] : check_list[u])
      if (color[v] != ccnt) found[p] = 0;
    if (((int)(arr).size()) == K - 1) {
      found[u] = 1;
      for (int i = 0; i < K - 1; i++)
        for (int j = 0; j < K - 1; j++)
          if (i != j && order[arr[i]] > order[arr[j]])
            check_list[arr[i]].push_back({arr[j], u});
    }
  }
  for (int i = 1; i <= N; i++)
    if (found[i]) {
      printf("2\n%d", i);
      for (int j : con[i])
        if (order[j] > order[i]) printf(" %d", j);
      puts("");
      return;
    }
  puts("-1");
}
int main() {
  int T;
  for (scanf("%d", &T); T--;) solve();
}