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 N = 100005;
int n, m, k;
vector<int> edges[N];
int deg[N];
bool removed[N];
int q[N];
void removeDegLessK(int k) {
  int front = 0, tail = 0;
  for (int i = 0; i < n; ++i) {
    deg[i] = edges[i].size();
    removed[i] = false;
    if (deg[i] < k) {
      q[tail++] = i;
      removed[i] = true;
    }
  }
  while (front < tail) {
    int u = q[front++];
    for (int v : edges[u]) {
      if (removed[v]) continue;
      if (--deg[v] < k) {
        removed[v] = true;
        q[tail++] = v;
      }
    }
  }
}
void sortAndCleanList() {
  for (int i = 0; i < n; ++i) {
    if (removed[i]) continue;
    for (int j = 0; j < edges[i].size(); ++j) {
      int v = edges[i][j];
      if (removed[v]) {
        edges[i][j] = edges[i].back();
        edges[i].pop_back();
        --j;
      }
    }
    sort(edges[i].begin(), edges[i].end());
  }
}
bool isClique(int u, int k) {
  if (deg[u] != k - 1) return false;
  vector<int> neighs;
  for (int v : edges[u]) {
    if (removed[v]) continue;
    neighs.push_back(v);
  }
  bool ret = true;
  for (int v : edges[u]) {
    if (removed[v]) continue;
    int cnt = 0;
    for (int w : neighs) {
      if (w == v) continue;
      if (!binary_search(edges[v].begin(), edges[v].end(), w)) break;
      ++cnt;
    }
    if (cnt != k - 2) {
      ret = false;
      break;
    }
  }
  return ret;
}
int solve() {
  scanf("%d %d %d", &n, &m, &k);
  for (int i = 0; i < n; ++i) edges[i].clear();
  for (int i = 0; i < m; ++i) {
    int u, v;
    scanf("%d %d", &u, &v);
    --u, --v;
    edges[u].push_back(v);
    edges[v].push_back(u);
  }
  removeDegLessK(k);
  vector<int> v;
  for (int i = 0; i < n; ++i) {
    if (!removed[i]) v.push_back(i);
  }
  if (v.size() > 0) {
    printf("1 %d\n", (int)v.size());
    for (int u : v) printf("%d ", u + 1);
    printf("\n");
    return 0;
  }
  removeDegLessK(k - 1);
  sortAndCleanList();
  int front = 0, tail = 0;
  for (int i = 0; i < n; ++i) {
    if (removed[i]) continue;
    if (deg[i] == k - 1) {
      q[tail++] = i;
    }
  }
  while (front < tail) {
    int u = q[front++];
    if (removed[u]) continue;
    if (isClique(u, k)) {
      printf("2\n");
      for (int v : edges[u])
        if (!removed[v]) {
          printf("%d ", v + 1);
        }
      printf("%d\n", u + 1);
      return 0;
    }
    removed[u] = true;
    for (int v : edges[u]) {
      if (removed[v]) continue;
      if (--deg[v] == k - 1) q[tail++] = v;
    }
  }
  printf("-1\n");
  return 0;
}
int main() {
  int t = 1;
  scanf("%d", &t);
  for (int tc = 0; tc < t; ++tc) {
    solve();
  }
  return 0;
}