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 PYTHON3):

Solution:
from collections import deque
import sys
input = sys.stdin.readline
for _ in range(int(input())):
    n, m, k = map(int, input().split())
    G = [set() for _ in range(n + 1)]
    deg = [0] * (n + 1)
    for _ in range(m):
        i, j = map(int, input().split())
        G[i].add(j)
        G[j].add(i)
        deg[i] += 1
        deg[j] += 1
    if k * (k - 1) > 2 * m:
        print(-1)
        continue
    q = deque()
    seen = [0] * (n + 1)
    for i in range(1, n + 1):
        if deg[i] < k:
            seen[i] = 1
            q.append(i)
    clique = []
    end = 0
    while q and not end:
        i = q.popleft()
        seen[i] = 2
        if deg[i] == k - 1 and not clique and k * (k - 1) // 2 <= m:
            clique = [i]
            for j in G[i]:
                if seen[j] <= 1:
                    clique.append(j)
            ok = 1
            for x in clique:
                for y in clique:
                    if x == y: break
                    if y not in G[x]:
                        ok = 0
                        break
                if not ok: break
            if not ok: clique = []
            else:
                print(2)
                print(*clique)
                end = 1
                break
        for j in G[i]:
            deg[j] -= 1
            if deg[j] < k and not seen[j]:
                seen[j] = 1
                q.append(j)
    if not end:
        subset = [i for i in range(1, n + 1) if not seen[i]]
        if subset:
            print("1 {}".format(len(subset)))
            print(*subset)
        else:
            print(-1)