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 mod = 1e9 + 7;
const int N = 1e5 + 7;
const long long inf = 1e18;
int n, m, k;
int du[N];
int vis[N];
unordered_map<int, int> mmp[N];
vector<int> son[N];
vector<int> v;
void init() {
  for (int i = 1; i <= n; i++)
    son[i].clear(), du[i] = 0, vis[i] = 0, mmp[i].clear();
}
bool check(int x) {
  v.clear();
  v.push_back(x);
  for (int i = 0; i < son[x].size(); i++) {
    int d = son[x][i];
    if (vis[d] < 2) v.push_back(d);
  }
  if (v.size() != k) return false;
  for (int i = 0; i < v.size() - 1; i++)
    for (int j = i + 1; j < v.size(); j++)
      if (!mmp[v[i]].count(v[j])) return false;
  return true;
}
void solve() {
  scanf("%d%d%d", &n, &m, &k);
  init();
  for (int i = 0; i < m; i++) {
    int a1, a2;
    scanf("%d%d", &a1, &a2);
    son[a1].push_back(a2);
    son[a2].push_back(a1);
    du[a1]++;
    du[a2]++;
    mmp[a1][a2] = 1;
    mmp[a2][a1] = 1;
  }
  if (k * (k - 1) > 2 * m) {
    printf("-1\n");
    return;
  }
  queue<int> q;
  for (int i = 1; i <= n; i++) {
    if (du[i] < k) q.push(i), vis[i] = 1;
  }
  while (q.size()) {
    auto a = q.front();
    q.pop();
    vis[a] = 2;
    if (du[a] == k - 1)
      if (check(a)) {
        printf("2\n");
        printf("%d ", a);
        for (int j = 0; j < son[a].size(); j++) {
          int d = son[a][j];
          if (vis[d] != 2) printf("%d ", d);
        }
        printf("\n");
        return;
      }
    for (int i = 0; i < son[a].size(); i++) {
      int d = son[a][i];
      du[d]--;
      if (vis[d]) continue;
      if (du[d] < k) q.push(d), vis[d] = 1;
    }
  }
  vector<int> ans;
  for (int i = 1; i <= n; i++)
    if (!vis[i]) ans.push_back(i);
  if (ans.size()) {
    printf("1 %d\n", ans.size());
    for (int i = 0; i < ans.size(); i++) printf("%d ", ans[i]);
    printf("\n");
  } else
    printf("-1\n");
}
int main() {
  int zs;
  scanf("%d", &zs);
  while (zs--) {
    solve();
  }
}