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 ll = long long int;
using int64 = long long int;
template <typename T>
void chmax(T &a, T b) {
  a = max(a, b);
}
template <typename T>
void chmin(T &a, T b) {
  a = min(a, b);
}
template <typename T>
void chadd(T &a, T b) {
  a = a + b;
}
int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
const int INF = 1LL << 29;
const ll LONGINF = 1LL << 60;
const ll MOD = 1000000007LL;
using Graph = vector<vector<int> >;
Graph calc(Graph G, int K) {
  set<pair<int, int> > S;
  int N = G.size();
  vector<int> deg(N);
  for (int i = 0; i < N; i++) {
    for (auto j : G[i]) {
      deg[j]++;
    }
  }
  for (int i = 0; i < N; i++) {
    S.emplace(deg[i], i);
  }
  vector<bool> exist(N, true);
  while (S.size() and S.begin()->first < K) {
    int u = S.begin()->second;
    exist[u] = false;
    S.erase(S.begin());
    for (int v : G[u]) {
      if (!exist[v]) continue;
      S.erase(make_pair(deg[v], v));
      deg[v]--;
      S.emplace(make_pair(deg[v], v));
    }
  }
  Graph H(N);
  for (int i = 0; i < N; i++) {
    for (auto j : G[i]) {
      if (exist[i] and exist[j]) H[i].emplace_back(j);
    }
  }
  return H;
}
struct UnionFind {
 private:
  const int n;
  int size_;
  vector<int> uf;

 public:
  UnionFind(int _n) : n(_n), size_(_n), uf(_n, -1) {}
  int find(int x) { return (uf[x] < 0) ? x : uf[x] = find(uf[x]); }
  bool same(int x, int y) { return find(x) == find(y); }
  int size(int x) { return -uf[find(x)]; }
  int size() { return size_; }
  bool unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y) return false;
    size_--;
    if (-uf[x] < -uf[y]) swap(x, y);
    uf[x] += uf[y];
    uf[y] = x;
    return true;
  }
};
void solve() {
  int N, M, K;
  scanf("%d%d%d", &N, &M, &K);
  Graph G(N);
  for (int i = 0; i < M; i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    u--;
    v--;
    G[u].emplace_back(v);
    G[v].emplace_back(u);
  }
  {
    Graph H = calc(G, K);
    UnionFind uf(N);
    for (int i = 0; i < N; i++) {
      for (auto j : H[i]) {
        uf.unite(i, j);
      }
    }
    for (int i = 0; i < N; i++) {
      if (uf.size(i) > K) {
        vector<int> ans;
        for (int j = 0; j < N; j++) {
          if (uf.same(i, j)) ans.emplace_back(j);
        }
        printf("1 %zu\n", ans.size());
        for (size_t j = 0; j < ans.size(); j++) {
          printf("%d%c", ans[j] + 1, " \n"[j + 1 == ans.size()]);
        }
        return;
      }
    }
  }
  {
    Graph H = calc(G, K - 1);
    vector<int> deg(N);
    for (int i = 0; i < N; i++) {
      sort(H[i].begin(), H[i].end());
      for (auto j : H[i]) {
        deg[j]++;
      }
    }
    set<pair<int, int> > S;
    for (int i = 0; i < N; i++) S.emplace(deg[i], i);
    vector<bool> exist(N, true);
    while (S.size() and S.begin()->first <= K - 1) {
      int u = S.begin()->second;
      S.erase(S.begin());
      if (deg[u] < K - 1) {
        exist[u] = false;
        for (auto v : H[u]) {
          if (!exist[v]) continue;
          S.erase(make_pair(deg[v], v));
          deg[v]--;
          S.emplace(deg[v], v);
        }
      } else {
        vector<int> vec;
        vec.emplace_back(u);
        for (auto v : H[u]) {
          if (!exist[v]) continue;
          vec.emplace_back(v);
        }
        bool ok = true;
        for (int i = 0; i < K; i++) {
          for (int j = i + 1; j < K; j++) {
            auto itr = lower_bound(H[vec[i]].begin(), H[vec[i]].end(), vec[j]);
            ok &= (itr != H[vec[i]].end() and *itr == vec[j]);
            if (!ok) i = j = K;
          }
        }
        if (ok) {
          printf("2\n");
          for (int i = 0; i < K; i++)
            printf("%d%c", vec[i] + 1, " \n"[i + 1 == K]);
          return;
        } else {
          exist[u] = false;
          for (auto v : H[u]) {
            if (!exist[v]) continue;
            S.erase(make_pair(deg[v], v));
            deg[v]--;
            S.emplace(deg[v], v);
          }
        }
      }
    }
  }
  puts("-1");
}
int main() {
  int T;
  scanf("%d", &T);
  while (T--) solve();
  return 0;
}