Ehab's Last Corollary

Description:

Input:

The first line contains three integers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$3 \le k \le n \le 10^5$$$, $$$n-1 \le m \le 2 \cdot 10^5$$$) — the number of vertices and edges in the graph, and the parameter $$$k$$$ from the statement.

Each of the next $$$m$$$ lines contains two integers $$$u$$$ and $$$v$$$ ($$$1 \le u,v \le n$$$) that mean there's an edge between vertices $$$u$$$ and $$$v$$$. It's guaranteed that the graph is connected and doesn't contain any self-loops or multiple edges.

Output:

If you choose to solve the first problem, then on the first line print $$$1$$$, followed by a line containing $$$\lceil\frac{k}{2}\rceil$$$ distinct integers not exceeding $$$n$$$, the vertices in the desired independent set.

If you, however, choose to solve the second problem, then on the first line print $$$2$$$, followed by a line containing one integer, $$$c$$$, representing the length of the found cycle, followed by a line containing $$$c$$$ distinct integers not exceeding $$$n$$$, the vertices in the desired cycle, in the order they appear in the cycle.

Sample Input:

4 4 3
1 2
2 3
3 4
4 1

Sample Output:

1
1 3 

Sample Input:

4 5 3
1 2
2 3
3 4
4 1
2 4

Sample Output:

2
3
2 3 4 

Sample Input:

4 6 3
1 2
2 3
3 4
4 1
1 3
2 4

Sample Output:

2
3
1 2 3 

Sample Input:

5 4 5
1 2
1 3
2 4
2 5

Sample Output:

1
1 4 5 

Note:

In the first sample:

Notice that printing the independent set $$$\{2,4\}$$$ is also OK, but printing the cycle $$$1-2-3-4$$$ isn't, because its length must be at most $$$3$$$.

In the second sample:

Notice that printing the independent set $$$\{1,3\}$$$ or printing the cycle $$$2-1-4$$$ is also OK.

In the third sample:

In the fourth sample: