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.

Difficulty: VERY_HARD
Tags: Graph algorithms

Data structures

Constructive algorithms
Skill types: Data structures

Starter code:

Solutions:
from __future__ import division, print_function
from heapq import *
import sys
le = sys.__stdin__.read().split('\n')[::-1]
af = []
for ezo in range(int(le.pop())):
	(n, m, k) = list(map(int, le.pop().split()))
	ar = [set() for _ in range(n)]
	for i in range(m):
		(a, b) = list(map(int, le.pop().split()))
		ar[a - 1].add(b - 1)
		ar[b - 1].add(a - 1)
	if k * (k - 1) > 2 * m:
		af.append(-1)
	else:
		pi = [i for i in range(n) if len(ar[i]) < k]
		re = set((i for i in range(n) if len(ar[i]) >= k))
		while pi:
			a = pi.pop()
			if len(ar[a]) == k - 1:
				clique = True
				for j in ar[a]:
					if clique:
						for h in ar[a]:
							if not h in ar[j] and h != j:
								clique = False
								break
				if clique:
					af.append(2)
					af.append(' '.join(map(str, [i + 1 for i in ar[a]] + [a + 1])))
					pi = []
					re = {-1}
			for j in ar[a]:
				ar[j].remove(a)
				if len(ar[j]) < k:
					if j in re:
						pi.append(j)
						re.discard(j)
		if re and re != {-1}:
			af.append('1' + ' ' + str(len(re)))
			af.append(' '.join(map(str, [i + 1 for i in re])))
		elif re != {-1}:
			af.append(-1)
print('\n'.join(map(str, af)))


from __future__ import division, print_function
from heapq import *
import sys
t = list(map(int, sys.stdin.readline().strip().split()))[0]
af = []
for _ in range(t):
	(n, m, k) = list(map(int, sys.stdin.readline().strip().split()))
	ar = [set() for _ in range(n)]
	for i in range(m):
		(a, b) = list(map(int, sys.stdin.readline().strip().split()))
		ar[a - 1].add(b - 1)
		ar[b - 1].add(a - 1)
	if k * (k - 1) > 2 * m:
		af.append(-1)
	else:
		pi = [i for i in range(n) if len(ar[i]) < k]
		re = set((i for i in range(n) if len(ar[i]) >= k))
		while pi:
			a = pi.pop()
			if len(ar[a]) == k - 1:
				clique = True
				for j in ar[a]:
					if clique:
						for h in ar[a]:
							if not h in ar[j] and h != j:
								clique = False
								break
				if clique:
					af.append(2)
					af.append(' '.join(map(str, [i + 1 for i in ar[a]] + [a + 1])))
					pi = []
					re = {-1}
			for j in ar[a]:
				ar[j].remove(a)
				if len(ar[j]) < k:
					if j in re:
						pi.append(j)
						re.discard(j)
		if re and re != {-1}:
			af.append('1' + ' ' + str(len(re)))
			af.append(' '.join(map(str, [i + 1 for i in re])))
		elif re != {-1}:
			af.append(-1)
print('\n'.join(map(str, af)))