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;
namespace Flandre_Scarlet {
int I() {
  char c = getchar();
  int x = 0;
  int f = 1;
  while (c < '0' or c > '9') f = (c == '-') ? -1 : 1, c = getchar();
  while (c >= '0' and c <= '9')
    x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
  return ((f == 1) ? x : -x);
}
template <typename T>
void Rd(T& arg) {
  arg = I();
}
template <typename T, typename... Types>
void Rd(T& arg, Types&... args) {
  arg = I();
  Rd(args...);
}
void RA(int* p, int n) {
  for (int i = 1; i <= n; ++i) *p = I(), ++p;
}
struct edge {
  int u, v;
};
vector<edge> E;
void ReadE(int m, int t = 2) {
  for (int i = 1; i <= m; ++i) E.push_back((edge){I(), I()});
}
vector<int> g[200005];
int n, m, k;
void Input() {
  Rd(n, m, k);
  ReadE(m);
  for (auto x : E) g[x.u].push_back(x.v), g[x.v].push_back(x.u);
  for (int i = 1; i <= n; ++i) sort(g[i].begin(), g[i].end());
}
int Q[200005], head = 1, tail = 0;
int deg[200005];
bool vis[200005], del[200005];
int ansk;
vector<int> ans, cliq;
inline bool cxk_clique(int u) {
  cliq.push_back(u);
  for (auto x : g[u])
    if (!del[x]) cliq.push_back(x);
  if (((int)cliq.size()) != k) return false;
  for (auto x : cliq)
    for (auto y : cliq) {
      if (x == y) break;
      if (!binary_search(g[x].begin(), g[x].end(), y)) {
        return false;
      }
    }
  ansk = 2;
  return true;
}
void TopoSort() {
  for (auto e : E) ++deg[e.v], ++deg[e.u];
  head = 1, tail = 0;
  for (int i = 1; i <= n; ++i)
    if (deg[i] < k) Q[++tail] = i, vis[i] = 1;
  while (head <= tail) {
    int u = Q[head++];
    if (deg[u] == k - 1) {
      if (cxk_clique(u))
        return;
      else
        cliq.clear();
    }
    del[u] = 1;
    for (auto v : g[u]) {
      --deg[v];
      if (deg[v] < k and !vis[v]) Q[++tail] = v, vis[v] = 1;
    }
  }
  ans.clear();
  for (int i = 1; i <= n; ++i)
    if (!vis[i]) ans.push_back(i);
  if (ansk == -1 and ((int)ans.size())) {
    ansk = 1;
  }
}
void Soviet() {
  if (1ll * k * (k - 1) > 2 * m) {
    puts("-1");
    return;
  }
  if (k == 1) {
    puts("2");
    puts("1");
    return;
  }
  ansk = -1;
  TopoSort();
  if (ansk == -1) {
    puts("-1");
    return;
  }
  if (ansk == 1) {
    printf("1 %d\n", ((int)ans.size()));
    for (auto x : ans) printf("%d ", x);
    puts("");
  }
  if (ansk == 2) {
    puts("2");
    for (auto x : cliq) printf("%d ", x);
    puts("");
  }
}
void clear() {
  E.clear();
  for (int i = 1; i <= n; ++i) g[i].clear();
  head = 1;
  tail = 0;
  for (int i = 1; i <= n; ++i) vis[i] = del[i] = deg[i] = 0;
  ans.clear();
  cliq.clear();
  ansk = -1;
}
void IsMyWife() {
  int t = I();
  while (t-- > 0) {
    Input();
    Soviet();
    clear();
  }
}
}  // namespace Flandre_Scarlet
int main() {
  Flandre_Scarlet::IsMyWife();
  getchar();
  return 0;
}