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 maxn = 1e5 + 5;
vector<int> g[maxn];
int deg[maxn], vis[maxn];
queue<int> q;
vector<int> c;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, m, k;
    c.clear();
    scanf("%d%d%d", &n, &m, &k);
    for (int i = 1; i <= n; ++i) g[i].clear();
    for (int i = 0; i < m; ++i) {
      int u, v;
      scanf("%d%d", &u, &v);
      g[u].push_back(v);
      g[v].push_back(u);
    }
    for (int i = 1; i <= n; ++i) {
      vis[i] = 0;
      deg[i] = g[i].size();
      sort(g[i].begin(), g[i].end());
      if (deg[i] < k) q.push(i);
    }
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      if (deg[u] == k - 1 && c.empty()) {
        bool ok = true;
        c.push_back(u);
        for (auto v : g[u]) {
          if (vis[v]) continue;
          if (deg[v] < k - 1) {
            ok = false;
            break;
          }
          c.push_back(v);
        }
        if (ok) {
          for (int i = 0; i < c.size(); ++i) {
            for (int j = 0; j < c.size(); ++j) {
              if (i == j) continue;
              int u = c[i], v = c[j];
              if (!binary_search(g[u].begin(), g[u].end(), v)) {
                ok = false;
                goto L;
              }
            }
          }
        L:;
        }
        if (!ok) c.clear();
      }
      vis[u] = 1;
      for (auto v : g[u]) {
        deg[v]--;
        deg[u]--;
        if (deg[v] == k - 1) q.push(v);
      }
    }
    vector<int> ans;
    for (int i = 1; i <= n; ++i)
      if (deg[i] >= k) ans.push_back(i);
    if (!ans.empty()) {
      printf("1 %d\n", (int)ans.size());
      for (auto u : ans) printf("%d ", u);
      puts("");
    } else if (!c.empty()) {
      printf("2\n");
      for (auto u : c) printf("%d ", u);
      puts("");
    } else
      printf("-1\n");
  }
}