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;
const int INF = 0x3f3f3f3f;
const int N = 1e5 + 10;
int vis[N], d[N], n, m, k;
vector<int> g[N];
void init() {
  for (int i = 0; i <= n; i++) {
    g[i].clear();
    d[i] = 0;
    vis[i] = 0;
  }
}
int main() {
  int t, i, j, x, y, flag;
  queue<int> que;
  vector<int> res;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d%d", &n, &m, &k);
    init();
    for (i = 0; i < m; i++) {
      scanf("%d%d", &x, &y);
      g[x].push_back(y);
      g[y].push_back(x);
    }
    for (i = 1; i <= n; i++) {
      sort(g[i].begin(), g[i].end());
      d[i] = g[i].size();
    }
    res.clear();
    for (i = 1; i <= n; i++) {
      if (d[i] <= k - 1) {
        vis[i] = 1;
        que.push(i);
      }
    }
    while (!que.empty()) {
      x = que.front();
      que.pop();
      vis[x] = 2;
      if (d[x] == k - 1 && res.empty() && 1ll * (k * (k - 1) / 2) <= m) {
        res.push_back(x);
        for (i = 0; i < g[x].size(); i++) {
          if (vis[g[x][i]] != 2) res.push_back(g[x][i]);
        }
        flag = 1;
        for (i = 0; i < res.size(); i++) {
          for (j = 0; j < res.size(); j++) {
            if (i != j &&
                !binary_search(g[res[i]].begin(), g[res[i]].end(), res[j]))
              flag = 0;
          }
        }
        if (!flag) res.clear();
      }
      for (i = 0; i < g[x].size(); i++) {
        y = g[x][i];
        d[y]--;
        if (d[y] <= k - 1 && !vis[y]) {
          vis[y] = 1;
          que.push(y);
        }
      }
    }
    int cnt = 0;
    for (i = 1; i <= n; i++) {
      if (vis[i] == 0) cnt++;
    }
    if (cnt) {
      printf("1 %d\n", cnt);
      for (i = 1; i <= n; i++) {
        if (vis[i] == 0) printf("%d ", i);
      }
      printf("\n");
    } else if (res.size() > 0) {
      printf("2\n");
      for (i = 0; i < res.size(); i++) {
        if (i)
          printf(" %d", res[i]);
        else
          printf("%d", res[i]);
      }
      printf("\n");
    } else
      printf("-1\n");
  }
  return 0;
}