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.

4 4 3
1 2
2 3
3 4
4 1

1
1 3

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

2
3
2 3 4

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

2
3
1 2 3

5 4 5
1 2
1 3
2 4
2 5

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: