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;
class GraphNode {
 public:
  void addNeighbor(int u) {
    neighbors_.push_back(u);
    degree_++;
  }
  void deleteNeighbor(int u) { degree_--; }
  void set_id(int id) { id_ = id; }
  int get_degree() { return degree_; }
  int get_id() { return id_; }
  bool isNeighbor(int u) {
    auto it = lower_bound(neighbors_.begin(), neighbors_.end(), u);
    return (u == id_) || (it != neighbors_.end() && *it == u);
  }
  bool visit() {
    bool v = visited_;
    visited_ = true;
    return v;
  }
  vector<int> neighbors_;

 private:
  int weight_, id_, degree_ = 0;
  bool visited_ = false;
};
class Graph {
 private:
  int maxNodeId = 0;

 public:
  vector<unique_ptr<GraphNode>> nodes_;
  int max_node_id_ = 0;
  int size() {
    int ans = 0;
    for (auto &node : nodes_)
      if (node) ans++;
    return ans;
  }
  bool empty() { return size() == 0; }
  void init() { maxNodeId = 0; }
  void cool() {
    for (auto &node : nodes_)
      if (node) sort(node->neighbors_.begin(), node->neighbors_.end());
  }
  void addNode(int u) {
    nodes_.emplace_back(unique_ptr<GraphNode>(new GraphNode()));
    nodes_[u]->set_id(u);
  }
  void addNode() {
    addNode(max_node_id_);
    max_node_id_++;
  }
  void deleteNode(int u) {
    if (!nodes_[u]) {
      cout << "ERROR: nodes not exist! ";
      cerr << "u"
           << "=" << u << endl;
      return;
    }
    for (int &nb : nodes_[u]->neighbors_) {
      if (nb == u) continue;
      if (nodes_[nb]) nodes_[nb]->deleteNeighbor(u);
    }
    nodes_[u] = NULL;
  }
  void deleteEdge(int u, int v) {
    nodes_[u]->deleteNeighbor(v);
    nodes_[v]->deleteNeighbor(u);
  }
  void addEdge(int u, int v) {
    nodes_[u]->addNeighbor(v);
    nodes_[v]->addNeighbor(u);
  }
  void printNodes() {
    for (auto &node : nodes_) {
      if (node) cout << node->get_id() << " ";
    }
    cout << endl;
  }
};
class myGraph : public Graph {
 public:
  string s2;
  std::queue<int> q_;
  void deleteNode(int u, int k) {
    if (!nodes_[u]) return;
    for (int &nb : nodes_[u]->neighbors_)
      if (nodes_[nb]) {
        nodes_[nb]->deleteNeighbor(u);
        if (nodes_[nb]->get_degree() == k - 1) q_.push(nb);
      }
    nodes_[u] = NULL;
  }
  bool check(int k, int &m) {
    for (auto &node : nodes_) {
      if (node && node->get_degree() < k) {
        q_.push(node->get_id());
      }
    }
    while (!q_.empty()) {
      if (nodes_[q_.front()]) m -= nodes_[q_.front()]->get_degree();
      deleteNode(q_.front(), k);
      q_.pop();
    }
    return size() > 0;
  }
  bool check2(int k, int &m) {
    for (auto &node : nodes_) {
      if (node && node->get_degree() < k) {
        q_.push(node->get_id());
      }
    }
    bool succ = false;
    while (!q_.empty()) {
      auto &node = nodes_[q_.front()];
      if (!succ && node && node->get_degree() == k - 1 &&
          (k - 1 <= 2 * m / k)) {
        succ = true;
        vector<int> nbs;
        for (auto &nb : node->neighbors_) {
          if (nodes_[nb]) nbs.emplace_back(nb);
        }
        for (int i = 0; i < k - 1; i++)
          if (succ) {
            for (int j = i + 1; j < k - 1; j++)
              succ &= nodes_[nbs[i]]->isNeighbor(nbs[j]);
          }
        if (succ) {
          s2 = "";
          for (auto &nb : nbs) s2 = s2 + to_string(nb) + " ";
          s2 = s2 + to_string(node->get_id());
        }
      }
      if (nodes_[q_.front()]) m -= nodes_[q_.front()]->get_degree();
      deleteNode(q_.front(), k);
      q_.pop();
    }
    return succ;
  }
};
int work() {
  myGraph g;
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 0; i <= n; i++) {
    g.addNode();
  }
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    g.addEdge(u, v);
  }
  g.cool();
  g.check(k - 1, m);
  bool b = g.check2(k, m);
  if (g.check(k, m)) {
    cout << 1 << " " << g.size() << endl;
    g.printNodes();
  } else if (b) {
    cout << 2 << endl;
    cout << g.s2 << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}
int main() {
  int T;
  cin >> T;
  while (T--) {
    work();
  }
  return 0;
}