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;
long long int gcd(long long int a, long long int b) {
  return (b == 0LL ? a : gcd(b, a % b));
}
long double dist(long double x, long double arayikhalatyan, long double x2,
                 long double y2) {
  return sqrt((x - x2) * (x - x2) +
              (arayikhalatyan - y2) * (arayikhalatyan - y2));
}
long long int S(long long int a) { return (a * (a + 1LL)) / 2LL; }
mt19937 rnd(363542);
char vow[] = {'a', 'e', 'i', 'o', 'u'};
int dx[] = {0, -1, 0, 1, -1, -1, 1, 1, 0};
int dy[] = {-1, 0, 1, 0, -1, 1, -1, 1, 0};
const int N = 5e5 + 30;
const long long int mod = 998244353;
const long double pi = acos(-1);
const long double e = 1e-13;
long long int bp(long long int a, long long int b = mod - 2LL) {
  long long int ret = 1;
  while (b) {
    if (b & 1) ret *= a, ret %= mod;
    a *= a;
    a %= mod;
    b >>= 1;
  }
  return ret;
}
ostream& operator<<(ostream& c, pair<int, int> a) {
  c << a.first << " " << a.second;
  return c;
}
struct pt {
  long long int x, y;
  int ind;
  int bl;
  bool operator==(const pt& a) { return ind == a.ind; }
  bool operator<(const pt& b) {
    if (x == b.x) return y < b.y;
    return x < b.x;
  }
};
int n, m, t, k;
vector<int> g[N];
int sz[N];
unordered_map<int, int> mp[N];
bool stg(int v) {
  vector<int> fp;
  for (int p : g[v])
    if (sz[p] >= k - 1) fp.push_back(p);
  for (int i = 0; i < fp.size(); i++)
    for (int j = i + 1; j < fp.size(); j++)
      if (!mp[fp[i]][fp[j]]) return 0;
  return 1;
}
void cl() {
  for (int i = 1; i <= n; i++) {
    mp[i].clear();
    g[i].clear();
    sz[i] = 0;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> t;
  while (t--) {
    cin >> n >> m >> k;
    for (int i = 0; i < m; i++) {
      int a, b;
      cin >> a >> b;
      mp[a][b] = 1;
      mp[b][a] = 1;
      g[a].push_back(b);
      g[b].push_back(a);
    }
    if (k > 500) {
      cout << -1 << endl;
      cl();
      continue;
    }
    queue<int> q, q1;
    for (int i = 1; i <= n; i++) {
      sz[i] = g[i].size();
      if (sz[i] < k) q.push(i);
    }
    int qn = n;
    while (q.size()) {
      int v = q.front();
      qn--;
      sz[v] = 0;
      q.pop();
      for (auto p : g[v]) {
        sz[p]--;
        if (sz[p] == k - 1) q.push(p);
      }
    }
    if (qn) {
      cout << 1 << " " << qn << endl;
      for (int i = 1; i <= n; i++)
        if (sz[i] >= k) cout << i << " ";
      cl();
      cout << "\n";
      continue;
    }
    for (int i = 1; i <= n; i++) {
      sz[i] = g[i].size();
      if (sz[i] < k - 1)
        q.push(i);
      else if (sz[i] == k - 1)
        q1.push(i);
    }
    bool bl = 0;
    while ((int)q.size() + (int)q1.size()) {
      if (q.size()) {
        int v = q.front();
        sz[v] = 0;
        q.pop();
        for (auto p : g[v]) {
          sz[p]--;
          if (sz[p] == k - 1)
            q1.push(p);
          else if (sz[p] == k - 2)
            q.push(p);
        }
      } else {
        int v = q1.front();
        q1.pop();
        if (sz[v] < k - 1) {
          continue;
        }
        if (stg(v)) {
          cout << 2 << endl;
          cout << v << " ";
          for (int p : g[v])
            if (sz[p] >= k - 1) cout << p << " ";
          cout << "\n";
          bl = 1;
          break;
        }
        q.push(v);
      }
    }
    if (!bl) cout << -1 << endl;
    cl();
  }
  return 0;
}