1439_B. Graph Subset 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.
```python
import sys
input = sys.stdin.readline
testcase = int(input())
for _ in range(testcase):
  n,m,k = map(int,input().split())
  ab = [list(map(int,input().split())) for i in range(m)]
  if k == 1:
    print(2)
    print(1)
    continue
  if k*(k-1) > 2*m:
    print(-1)
    continue
  graph = [set() for i in range(n+1)]
  for a,b in ab:
    graph[a].add(b)
    graph[b].add(a)
  trash = set()
  stack = []
  for i in range(1,n+1):
    if len(graph[i]) < k-1:
      trash.add(i)
      stack.append(i)
  while stack:
    x = stack.pop()
    for y in graph[x]:
      if x in graph[y]:
        graph[y].remove(x)
        if len(graph[y]) < k-1:
          stack.append(y)
          trash.add(y)
    graph[x] = set()
  if n-len(trash) < k:
    print(-1)
    continue
  ansflg = 0
  ccand = []
  for i in range(1,n+1):
    if len(graph[i]) == k-1:
      ccand.append(i)
  while ccand:
    x = ccand.pop()
    if len(graph[x]) < k-1:
      trash.add(x)
      for y in graph[x]:
        if x in graph[y]:
          graph[y].remove(x)
          if len(graph[y]) == k-1:
            ccand.append(y)
      graph[x] = set()
      continue
    lsg = list(graph[x])
    for i in range(len(lsg)-1):
      for j in range(i+1,len(lsg)):
        if lsg[j] not in graph[lsg[i]]:
          trash.add(x)
          for y in graph[x]:
            if x in graph[y]:
              graph[y].remove(x)
              if len(graph[y]) == k-1:
                ccand.append(y)
          graph[x] = set()
          break
      else:
        continue
      break
    else:
      ansflg = 1
      break
  if ansflg:
    print(2)
    graph[x].add(x)
    print(*graph[x])
  elif n-len(trash) >= k+1:
    ansls = []
    for i in range(1,n+1):
      if i not in trash:
        ansls.append(i)
    print(1,len(ansls))
    print(*ansls)
  else:
    print(-1)
```