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;
long long t, n, m, k, u[1000005], v[1000005], first[1000005], nxt[1000005];
bool book[30000005];
long long du[1000005], del[1000005];
long long q[1000005], head, tail;
long long tot, c[1000005];
signed main() {
  cin >> t;
  while (t--) {
    cin >> n >> m >> k;
    for (long long i = 1; i <= m; i++) {
      scanf("%lld%lld", &u[i], &v[i]);
      nxt[i] = first[u[i]], first[u[i]] = i;
      u[i + m] = v[i], v[i + m] = u[i];
      nxt[i + m] = first[u[i + m]], first[u[i + m]] = i + m;
      du[u[i]]++, du[v[i]]++;
      book[(u[i] * n + v[i]) % 29999997] = book[(v[i] * n + u[i]) % 29999997] =
          1;
    }
    long long fg = 1;
    if (k * (k - 1) <= m * 2) {
      head = 1, tail = 0;
      for (long long i = 1; i <= n; i++)
        if (du[i] < k) q[++tail] = i;
      while (head <= tail) {
        long long now = q[head];
        ++head;
        if (du[now] == k - 1) {
          tot = 0;
          c[++tot] = now;
          for (register long long i = first[now]; i; i = nxt[i])
            if (del[v[i]] == 0) c[++tot] = v[i];
          long long nowfg = 1;
          for (register long long i = 1; i <= tot; i++)
            for (register long long j = 1; j < i; j++)
              if (book[(c[i] * n + c[j]) % 29999997] == 0) nowfg = 0;
          if (nowfg == 1) {
            if (fg == 1) {
              puts("2");
              for (register long long i = 1; i <= tot; i++)
                printf("%lld ", c[i]);
              puts("");
              fg = 0;
            }
          }
        }
        del[now] = 1;
        for (register long long i = first[now]; i; i = nxt[i]) {
          du[v[i]]--;
          if (du[v[i]] == k - 1) q[++tail] = v[i];
        }
      }
      tot = 0;
      for (register long long i = 1; i <= n; i++)
        if (del[i] == 0 && du[i] >= k) c[++tot] = i;
      if (tot > 0 && fg == 1) {
        printf("1 %lld\n", tot);
        for (register long long i = 1; i <= tot; i++) printf("%lld ", c[i]);
        puts("");
        fg = 0;
      }
    }
    if (fg == 1) puts("-1");
    for (long long i = 1; i <= 2 * m; i++) {
      nxt[i] = 0;
      book[(u[i] * n + v[i]) % 29999997] = 0;
      u[i] = v[i] = 0;
    }
    for (long long i = 1; i <= n; i++) first[i] = du[i] = del[i] = 0;
  }
  return 0;
}