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;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using lpair = std::pair<ll, ll>;
const int _ = []() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
  std::cout << std::fixed << std::setprecision(10);
  return 0;
}();
template <typename value_t>
void resize(value_t& v, const value_t& val) {
  v = val;
}
template <typename vec_t, typename value_t, typename... arg_t>
void resize(std::vector<vec_t>& v, const value_t& val, int size, arg_t... arg) {
  v.resize(size);
  for (auto& c : v) resize(c, val, arg...);
}
template <typename A, typename B>
void chmin(A& a, const B& b) {
  a = min(a, static_cast<A>(b));
};
template <typename A, typename B>
void chmax(A& a, const B& b) {
  a = max(a, static_cast<A>(b));
};
void query() {
  ll n, m, k;
  cin >> n >> m >> k;
  vector<unordered_set<ll>> link(n);
  for (ll i = 0; i < m; ++i) {
    ll a, b;
    cin >> a >> b;
    --a;
    --b;
    link[a].insert(b);
    link[b].insert(a);
  }
  priority_queue<lpair, vector<lpair>, greater<lpair>> q;
  for (ll i = 0; i < n; ++i) {
    q.push({link[i].size(), i});
  }
  while (!q.empty()) {
    auto [sz, ind] = q.top();
    if (sz >= k) break;
    q.pop();
    if (link[ind].size() != sz) continue;
    if (sz == k - 1 && k * (k - 1) <= 2 * m) {
      bool ok = true;
      for (ll c : link[ind]) {
        for (ll d : link[ind]) {
          if (c != d && link[c].count(d) == 0) {
            ok = false;
            break;
          }
        }
        if (!ok) break;
      }
      if (ok) {
        cout << "2 " << (ind + 1) << endl;
        for (ll x : link[ind]) {
          cout << (x + 1) << " ";
        }
        cout << endl;
        return;
      }
    }
    auto it = link[ind].begin();
    while (it != link[ind].end()) {
      link[*it].erase(ind);
      q.push({link[*it].size(), *it});
      it = link[ind].erase(it);
    }
  }
  vector<ll> v;
  for (ll i = 0; i < n; ++i) {
    if (link[i].size() >= k) v.push_back(i);
  }
  if (!v.empty()) {
    cout << "1 " << v.size() << endl;
    for (ll x : v) {
      cout << (1 + x) << " ";
    }
    cout << endl;
  } else {
    cout << -1 << endl;
  }
}
int main() {
  ll t;
  cin >> t;
  while (t--) {
    query();
  }
  return 0;
}