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 N = 100000;
struct side0 {
  int x, y;
  side0(int X = 0, int Y = 0) {
    x = X;
    y = Y;
  }
  bool operator<(const side0 &p) const {
    return x < p.x || x == p.x && y < p.y;
  }
};
set<side0> s;
int n, m, sk;
vector<int> e[N + 9];
int deg[N + 9];
void into() {
  scanf("%d%d%d", &n, &m, &sk);
  s.clear();
  for (int i = 1; i <= n; ++i) {
    deg[i] = 0;
    e[i].clear();
  }
  for (int i = 1; i <= m; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    if (x > y) swap(x, y);
    if (x == y) continue;
    if (s.find(side0(x, y)) != s.end()) continue;
    e[x].push_back(y);
    e[y].push_back(x);
    ++deg[x];
    ++deg[y];
    s.insert(side0(x, y));
  }
  for (int i = 1; i <= n; ++i) sort(e[i].begin(), e[i].end());
}
int vis[N + 9];
vector<int> ans;
bool Check_ans() {
  for (auto x : ans)
    for (auto y : ans)
      if (x ^ y && !binary_search(e[x].begin(), e[x].end(), y)) return 0;
  printf("2\n");
  for (auto x : ans) printf("%d ", x);
  puts("");
  return 1;
}
queue<int> q;
void Get_ans() {
  for (; !q.empty(); q.pop())
    ;
  for (int i = 1; i <= n; ++i) {
    vis[i] = 0;
    if (deg[i] < sk) vis[i] = 1, q.push(i);
  }
  for (; !q.empty();) {
    int t = q.front();
    q.pop();
    vis[t] = 2;
    if (deg[t] == sk - 1 && (long long)sk * (sk - 1) <= m << 1) {
      ans.clear();
      ans.push_back(t);
      for (auto y : e[t])
        if (vis[y] < 2) ans.push_back(y);
      if (Check_ans()) return;
    }
    for (auto y : e[t])
      if (--deg[y] < sk && !vis[y]) vis[y] = 1, q.push(y);
  }
  ans.clear();
  for (int i = 1; i <= n; ++i)
    if (!vis[i]) ans.push_back(i);
  if (!ans.empty()) {
    printf("1 %d\n", ans.size());
    for (auto x : ans) printf("%d ", x);
    puts("");
    return;
  }
  puts("-1");
}
void work() { Get_ans(); }
void outo() {}
int main() {
  int T = 1;
  scanf("%d", &T);
  for (; T--;) {
    into();
    work();
    outo();
  }
  return 0;
}