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;
inline int read() {
  int x = 0, f = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 1) + (x << 3) + (c ^ 48);
    c = getchar();
  }
  return f == 1 ? x : -x;
}
const int N = 1e5 + 4;
int n, m, k, cou, fl, deg[N], del[N], st[N];
vector<int> e[N];
queue<int> q;
void solve() {
  n = read();
  m = read();
  k = read();
  cou = 0;
  for (int i = 0; i <= n; i++) deg[i] = del[i] = 0;
  for (int i = 1; i <= n; i++) e[i].clear();
  while (!q.empty()) q.pop();
  for (int i = 1, u, v; i <= m; i++) {
    u = read();
    v = read();
    e[u].push_back(v);
    e[v].push_back(u);
    deg[u]++;
    deg[v]++;
  }
  for (int i = 1; i <= n; i++) sort(e[i].begin(), e[i].end());
  for (int i = 1; i <= n; i++)
    if (deg[i] < k) {
      del[i] = 1;
      q.push(i);
    }
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    cou++;
    if (deg[x] == k - 1) {
      st[0] = 0;
      for (auto v : e[x])
        if (deg[v] >= k - 1) {
          st[++st[0]] = v;
        }
      if (st[0] == k - 1) {
        fl = 1;
        for (int i = 1; i <= st[0] && fl; i++) {
          for (int j = 1; j < i; j++) {
            auto it = lower_bound(e[st[i]].begin(), e[st[i]].end(), st[j]);
            if (it == e[st[i]].end() || (*it) != st[j]) {
              fl = 0;
              break;
            }
          }
        }
        if (fl) {
          cout << "2\n" << x << " ";
          for (int i = 1; i <= st[0]; i++) cout << st[i] << " ";
          puts("");
          return;
        }
      }
    }
    deg[x] = -1;
    for (auto v : e[x]) {
      deg[v]--;
      if (!del[v] && deg[v] < k) {
        del[v] = 1;
        q.push(v);
      }
    }
  }
  if (cou != n) {
    cout << "1 " << n - cou << "\n";
    for (int i = 1; i <= n; i++)
      if (!del[i]) cout << i << " ";
    puts("");
  } else
    puts("-1");
}
int main() {
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}