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 MAXN = 2e5 + 10;
const int MAXM = 4e6 + 10;
const long long MOD = 998244353;
const long long INF = 0x3f3f3f3f;
const unsigned long long BASE = 233;
const int base = 5;
mt19937_64 mt(time(0));
char rubbish[110];
bool GETDATA;
bool PRINT;
inline long long read() {
  long long x = 0, f = 1;
  char ch;
  do {
    ch = getchar();
    if (ch == '-') f = -1;
  } while (ch < '0' || ch > '9');
  do {
    x = x * 10 + ch - 48;
    ch = getchar();
  } while (ch >= '0' && ch <= '9');
  return x * f;
}
inline void write(long long x, char con = '\n') {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10, 0);
  putchar(x % 10 + '0');
  if (con) putchar(con);
}
long long N, M, K, Q;
long long a[MAXN];
unordered_set<int> es[MAXN];
priority_queue<pair<int, int> > pq;
vector<int> res;
void init() {
  for (int i = 1; i <= N; i++) {
    es[i].clear();
  }
  while (!pq.empty()) {
    pq.pop();
  }
  res.clear();
}
void solve() {
  long long ans = 0;
  bool able;
  int u, v;
  N = read();
  M = read();
  K = read();
  init();
  for (int i = 1; i <= M; i++) {
    u = read();
    v = read();
    es[u].insert(v);
    es[v].insert(u);
  }
  if (K == 1) {
    write(2);
    write(1);
    return;
  }
  if (K > 450) {
    write(-1);
    return;
  }
  for (int i = 1; i <= N; i++) {
    pq.push(pair<int, int>(-es[i].size(), i));
  }
  able = false;
  while (!pq.empty()) {
    u = pq.top().second;
    pq.pop();
    if (es[u].empty()) {
      continue;
    }
    if (es[u].size() >= K) {
      able = true;
      break;
    }
    if (K * (K - 1) / 2 <= M && es[u].size() == K - 1) {
      able = true;
      for (auto p = es[u].begin(); able && p != es[u].end(); ++p) {
        for (auto q = p; able && ++q != es[u].end();) {
          if (!es[*p].count(*q)) {
            able = false;
          }
        }
      }
      if (able) {
        res.push_back(u);
        for (auto v : es[u]) {
          res.push_back(v);
        }
        break;
      }
    }
    for (auto v : es[u]) {
      es[v].erase(u);
      pq.push(pair<int, int>(-es[v].size(), v));
    }
    es[u].clear();
  }
  if (!res.empty()) {
    write(2);
    for (int i = 0; i < res.size(); i++) {
      write(res[i], i == res.size() - 1 ? '\n' : ' ');
    }
  } else if (able) {
    for (int i = 1; i <= N; i++) {
      if (!es[i].empty()) {
        res.push_back(i);
      }
    }
    write((1), ' ');
    write(res.size());
    for (int i = 0; i < res.size(); i++) {
      write(res[i], i == res.size() - 1 ? '\n' : ' ');
    }
  } else {
    write(-1);
  }
}
int main() {
  int T;
  T = 1;
  T = read();
  GETDATA = false;
  for (int t = 1; t <= T; t++) {
    PRINT = false;
    solve();
  }
  return 0;
}