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 std::binary_search;
using std::queue;
using std::sort;
using std::vector;
namespace MyIO {
const int MAXB = 1 << 10;
char gbuf[MAXB], *ps = gbuf, *pt = gbuf;
char pbuf[MAXB + 1], *pp = pbuf;
struct Flusher {
  ~Flusher() { fwrite(pbuf, 1, pp - pbuf, stdout); }
} flusher;
inline char Getchar() {
  if (ps == pt) {
    ps = gbuf;
    pt = gbuf + fread(gbuf, 1, MAXB, stdin);
  }
  return (ps == pt) ? EOF : *ps++;
}
inline void Putchar(const char &ch) {
  if (pp == pbuf + MAXB) {
    pp = pbuf;
    fwrite(pbuf, 1, MAXB, stdout);
  }
  *pp++ = ch;
}
}  // namespace MyIO
int read() {
  int x = 0;
  char c = MyIO::Getchar();
  bool f = 0;
  while (c < '0' || c > '9')
    (c == '-') ? f = 1, c = MyIO::Getchar() : c = MyIO::Getchar();
  while (c >= '0' && c <= '9')
    x = (x << 1) + (x << 3) + (48 ^ c), c = MyIO::Getchar();
  return (f) ? -x : x;
}
void write(const int &x) {
  if (x / 10) write(x / 10);
  MyIO::Putchar('0' + x % 10);
}
int main() {
  for (int t = 0, T = read(); t < T; ++t) {
    int n = read(), m = read(), k = read();
    vector<vector<int> > E(n);
    for (int i = 0; i < m; ++i) {
      int u = read() - 1, v = read() - 1;
      E[u].push_back(v), E[v].push_back(u);
    }
    vector<int> d(n), vis(n);
    for (int i = 0; i < n; ++i) {
      d[i] = E[i].size();
      sort(E[i].begin(), E[i].end());
    }
    queue<int> que;
    for (int i = 0; i < n; ++i)
      if (d[i] < k) {
        que.push(i);
        vis[i] = 1;
      }
    vector<int> cilque;
    while (!que.empty() && cilque.empty()) {
      int u = que.front();
      que.pop();
      vis[u] = 2;
      if (1ll * (k - 1) * k / 2 <= m && d[u] == k - 1 && cilque.empty()) {
        cilque.push_back(u);
        for (int v : E[u])
          if (vis[v] != 2) cilque.push_back(v);
        bool OK = 1;
        for (int v : cilque) {
          for (int w : cilque) {
            if (v == w)
              break;
            else if (!binary_search(E[v].begin(), E[v].end(), w)) {
              OK = 0;
              break;
            }
          }
          if (!OK) break;
        }
        if (!OK) cilque.clear();
      }
      for (int v : E[u])
        if (--d[v] == k - 1 && vis[v] == 0) {
          vis[v] = 1;
          que.push(v);
        }
    }
    if (!cilque.empty()) {
      MyIO::Putchar('2'), MyIO::Putchar('\n');
      for (int u : cilque) write(u + 1), MyIO::Putchar(' ');
      MyIO::Putchar('\n');
    } else if (count(vis.begin(), vis.end(), 0) > 0) {
      vector<int> ans;
      for (int i = 0; i < n; ++i)
        if (vis[i] == 0) ans.push_back(i);
      MyIO::Putchar('1'), MyIO::Putchar(' '), write(ans.size()),
          MyIO::Putchar('\n');
      for (int u : ans) write(u + 1), MyIO::Putchar(' ');
      MyIO::Putchar('\n');
    } else
      MyIO::Putchar('-'), MyIO::Putchar('1'), MyIO::Putchar('\n');
  }
}