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() {
  char ch = getchar();
  int x = 0, f = 1;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 1) + (x << 3) - '0' + ch;
    ch = getchar();
  }
  return x * f;
}
const int N = 1e5 + 10;
vector<int> g[N], c;
int n, m, k;
int st[N], d[N], t, q[N];
void solve() {
  n = read(), m = read(), k = read();
  int tot = n;
  for (int i = 1; i <= n; i++) g[i].clear(), st[i] = 0, d[i] = 0;
  for (int i = 1; i <= m; i++) {
    int a = read(), b = read();
    g[a].push_back(b);
    g[b].push_back(a);
    d[a]++, d[b]++;
  }
  if (k * (k - 1) > 2 * m) {
    puts("-1");
    return;
  }
  int hh = 0, tt = -1;
  for (int i = 1; i <= n; i++) sort(g[i].begin(), g[i].end());
  for (int i = 1; i <= n; i++) {
    if (d[i] < k) {
      q[++tt] = i;
      st[i] = 1;
      tot--;
    }
  }
  while (hh <= tt) {
    int t = q[hh++];
    if (st[t] == 2) continue;
    st[t] = 2;
    if (d[t] == k - 1) {
      c.clear();
      c.push_back(t);
      for (auto &j : g[t]) {
        if (st[j] == 2) continue;
        c.push_back(j);
      }
      bool ff = 0;
      for (auto &p : c) {
        for (auto &q : c) {
          if (p == q) continue;
          if (!binary_search(g[p].begin(), g[p].end(), q)) {
            ff = 1;
            break;
          }
        }
      }
      if (ff == 0) {
        puts("2");
        for (auto &x : c) {
          printf("%d ", x);
        }
        puts("");
        return;
      }
    }
    for (auto &j : g[t]) {
      d[j]--;
      if (st[j]) continue;
      if (d[j] < k) {
        q[++tt] = j;
        st[j] = 1;
        tot--;
      }
    }
  }
  if (tot > 0) {
    printf("%d %d\n", 1, tot);
    for (int i = 1; i <= n; i++) {
      if (!st[i]) {
        printf("%d ", i);
      }
    }
    puts("");
  } else {
    puts("-1");
  }
}
int main() {
  t = read();
  while (t--) solve();
}