Problem: Given a connected undirected graph with n vertices and an integer k, you have to either:

  * either find an independent set that has exactly ⌈k/2⌉ vertices.
  * or find a simple cycle of length at most k. 



An independent set is a set of vertices such that no two of them are connected by an edge. A simple cycle is a cycle that doesn't contain any vertex twice. 

I have a proof that for any input you can always solve at least one of these problems, but it's left as an exercise for the reader.

Input

The first line contains three integers n, m, and k (3 ≤ k ≤ n ≤ 10^5, n-1 ≤ m ≤ 2 ⋅ 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 ≤ u,v ≤ 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 ⌈k/2⌉ 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.

Examples

Input


4 4 3
1 2
2 3
3 4
4 1


Output


1
1 3 

Input


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


Output


2
3
2 3 4 

Input


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


Output


2
3
1 2 3 

Input


5 4 5
1 2
1 3
2 4
2 5


Output


1
1 4 5 

Note

In the first sample:

<image>

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:

<image>

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

In the third sample:

<image>

In the fourth sample:

<image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.LinkedList;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author xwchen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        final int N = 100005;
        int[] vis = new int[N];
        Graph g;
        int[] par = new int[N];
        int k;
        Vector<Integer>[] color = new Vector[2];
        Vector<Integer> res = new Vector<>();

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            k = in.nextInt();
            color[0] = new Vector<Integer>();
            color[1] = new Vector<Integer>();
            g = new Graph(n);
            for (int i = 0; i < m; ++i) {
                int u = in.nextInt();
                int v = in.nextInt();
                g.addEdge(u, v);
            }
            int Q = (k + 1) / 2;
            Arrays.fill(vis, 1 << 30);
            dfs(0, 1, 1);
            if (!res.isEmpty() && res.size() <= k) {
                out.println(2);
                out.println(res.size());
                for (int x : res) {
                    out.print(x + " ");
                }
            } else {
                out.println(1);
                Vector<Integer> iSet = color[0].size() > color[1].size() ? color[0] : color[1];
                //out.println(String.format("%d : %d", color[0].size(), color[1].size()));
                for (int i = 0; i < Q && i < iSet.size(); ++i) {
                    out.print(iSet.get(i) + " ");
                }
            }
        }

        void dfs(int pre, int cur, int depth) {
            if (!res.isEmpty() && res.size() <= k) {
                return;
            }
            vis[cur] = depth;
            color[depth % 2].add(cur);
            par[cur] = pre;
            for (Graph.Edge e : g.adj[cur]) {
                int v = e.v;
                if (v == pre) continue;
                if (vis[v] == 1 << 30) {
                    dfs(cur, v, depth + 1);
                } else if (vis[cur] - vis[v] <= k && vis[cur] > vis[v]) {
                    int root = cur;
                    //System.out.println("v = " + v);
                    if (!res.isEmpty() && res.size() <= k) {
                        return;
                    }
                    res.add(v);
                    while (root != v) {
                        res.add(root);
                        //System.out.println(String.format("parent %d = %d", root, par[root]));
                        root = par[root];
                    }
                    if (res.size() <= k) {
                        //System.out.println("OKK");
                        return;
                    } else {
                        res.clear();
                    }
                }
            }
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public InputReader(InputStream inputStream) {
            this.reader = new BufferedReader(
                    new InputStreamReader(inputStream));
        }

        public String next() {
            while (!tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class Graph {
        public LinkedList<Edge>[] adj;
        int n;

        public Graph() {

        }

        public Graph(int n) {
            this.n = n;
            adj = new LinkedList[n + 1];
            for (int i = 0; i <= n; ++i) {
//            adj[i] = new TreeSet<>((o1, o2) -> {
//                if (o1.value != o2.value) {
//                    return o1.value - o2.value;
//                } else {
//                    return o1.type - o2.type;
//                }
//            });
                adj[i] = new LinkedList<>();
            }
        }

        public void addEdge(int u, int v) {

            adj[u].add(new Edge(v, 1));
            adj[v].add(new Edge(u, 1));
            //System.out.println("add edge "+u+" "+v);
        }

        public class Edge {
            public int u;
            public int v;
            public int value;
            public int type;

            public Edge(int u, int v, int value, int type) {
                this.u = u;
                this.v = v;
                this.value = value;
                this.type = type;
            }

            public Edge(int u, int v, int value) {
                this.u = u;
                this.v = v;
                this.value = value;
            }

            public Edge(int v, int value) {
                this.v = v;
                this.value = value;
            }

        }

    }
}