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 = 2e5 + 10, size = 1 << 20, mod = 998244353, inf = 2e9;
const long long INF = 1e15;
template <class o>
void qr(o& x) {
  char c = getchar();
  x = 0;
  int f = 1;
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) x = x * 10 + c - '0', c = getchar();
  x *= f;
}
template <class o>
void qw(o x) {
  if (x / 10) qw(x / 10);
  putchar(x % 10 + '0');
}
template <class o>
void pr1(o x) {
  if (x < 0) x = -x, putchar('-');
  qw(x);
  putchar(' ');
}
template <class o>
void pr2(o x) {
  if (x < 0) x = -x, putchar('-');
  qw(x);
  putchar('\n');
}
long long gcd(long long a, long long b) { return !a ? b : gcd(b % a, a); }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long power(long long a, long long b = mod - 2, long long p = mod) {
  long long c = 1;
  while (b) {
    if (b & 1) c = c * a % p;
    b /= 2;
    a = a * a % p;
  }
  return c;
}
template <class o>
void cmax(o& x, o y) {
  if (x < y) x = y;
}
template <class o>
void cmin(o& x, o y) {
  if (x > y) x = y;
}
template <typename t1, typename t2>
void ad(t1& x, t2 y) {
  x += y;
  if (x >= mod) x -= mod;
}
template <typename t1, typename t2>
void dl(t1& x, t2 y) {
  x -= y;
  if (x < 0) x += mod;
}
template <typename T>
struct BIT {
  T* c;
  int n;
  BIT(int _n) : n(_n) {
    c = new T[n];
    c--;
    for (int i = 1; i <= n; i++) c[i] = T(0);
  }
  void add(int x, T y) {
    for (; x <= n; x += x & -x) c[x] = c[x] + y;
  }
  T sum(int x) {
    T y = T(0);
    for (; x; x &= x - 1) y = y + c[x];
    return y;
  }
};
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
  size_t operator()(pair<int, int> x) const {
    return operator()(uint64_t(x.first) << 32 | x.second);
  }
};
int n, m, k, deg[N], Q[N], l, r;
vector<int> e[N];
unordered_set<int, custom_hash> s[N];
bool del[N];
bool check(int x) {
  del[x] = 1;
  Q[++r] = x;
  static int q[N], tot;
  q[tot = 0] = x;
  for (int y : e[x])
    if (!del[y]) q[++tot] = y;
  if (tot + 1 != k) return 0;
  for (int i = 1; i <= tot; i++)
    for (int j = i + 1; j <= tot; j++)
      if (s[q[i]].count(q[j]) == 0) return 0;
  puts("2");
  for (int i = 0; i <= tot; i++) pr1(q[i]);
  puts("");
  return 1;
}
void solve() {
  qr(n);
  qr(m);
  qr(k);
  l = 1;
  r = 0;
  for (int i = 1; i <= n; i++) e[i].clear(), s[i].clear(), del[i] = 0;
  for (int i = 1; i <= m; i++) {
    int x, y;
    qr(x);
    qr(y);
    e[x].push_back(y);
    e[y].push_back(x);
    if (x < y)
      s[x].insert(y);
    else
      s[y].insert(x);
  }
  if (1LL * k * (k - 1) / 2 > m) {
    puts("-1");
    return;
  }
  for (int i = 1; i <= n; i++) {
    deg[i] = ((int)e[i].size());
    sort(e[i].begin(), e[i].end());
    if (deg[i] < k && check(i)) return;
  }
  while (l <= r) {
    int x = Q[l++];
    for (int y : e[x])
      if (!del[y]) {
        --deg[y];
        --m;
        if (deg[y] < k && check(y)) return;
      }
    if (1LL * k * (k - 1) / 2 > m) {
      puts("-1");
      return;
    }
  }
  int cnt = 0;
  for (int i = 1; i <= n; i++) cnt += !del[i];
  if (cnt) {
    printf("1 %d\n", cnt);
    for (int i = 1; i <= n; i++)
      if (!del[i]) pr1(i);
    puts("");
  } else
    puts("-1");
}
int main() {
  int T = 1;
  qr(T);
  while (T--) solve();
  return 0;
}