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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.*;

public class D {
    private static boolean check = false;
    private static List<Integer> dfs(ArrayList<Integer>[] graph, int[] colors, int[] colorCount, Integer current, int[] depths, int currentDepth, int parent, int k, boolean[] visited){
        int currentColor = 0;
        HashSet<Integer> set = new HashSet<>();
        if(graph[current] != null){
            for(int next : graph[current]){
                if(colors[next] != -1){
                    set.add(colors[next]);
                }
            }
        }
        visited[current] = true;
        depths[current] = currentDepth;
        currentDepth++;
        while (set.contains(currentColor)){
            currentColor++;
        }
        colors[current] = currentColor;
        colorCount[currentColor]++;
        List<Integer> response = null;
        if(graph[current] != null){
            for(int next : graph[current]){
                if(!visited[next]){
                    visited[next] = true;
                    response = dfs(graph, colors, colorCount, next, depths, currentDepth, current, k, visited);
                    if(response == null) check = false;
                    if(response != null && !response.get(0).equals(current) && !check){
                        response.add(current);
                        break;
                    }else if(response != null && response.get(0).equals(current)){
                        check = true;
                        break;
                    }
                    if(check){
                        break;
                    }
                }else if(next != parent && parent != -1){
                    if(depths[next] != -1 && depths[current] - depths[next] <= k - 1){
                        // found a cycle
                        List<Integer> s = new ArrayList<>();
                        s.add(next);
                        s.add(current);
                        depths[current] = -1;
                        return s;
                    }
                }
            }
        }
        depths[current] = -1;
        return response;
    }
    public static void main(String[] args) throws IOException{
        Reader sc = new Reader();
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        ArrayList<Integer>[] graph = new ArrayList[n];
        for(int i = 0; i < m; i++){
            int x = sc.nextInt();
            int y = sc.nextInt();
            if(graph[x-1] == null) graph[x-1] = new ArrayList<>();
            if(graph[y-1] == null) graph[y-1] = new ArrayList<>();
            graph[x-1].add(y-1);
            graph[y-1].add(x-1);
        }
        int[] colors = new int[n];
        int[] colorCount = new int[n];
        int[] depths = new int[n];
        boolean[] visited = new boolean[n];
        Arrays.fill(colors, -1);
        Arrays.fill(depths, -1);
        List<Integer> cycle = dfs(graph, colors, colorCount, 0, depths, 0, -1, k, visited);
        StringBuilder sb = new StringBuilder();
        if(cycle == null){
            int req = (int) Math.ceil(k/(2.0));
            int color = -1;
            for(int i = 0; i < n; i++){
                if(colorCount[i] >= req){
                    color = i;
                    break;
                }
            }
            sb.append(1).append("\n");
            int count = 0;
            for(int i = 0; i < n; i++){
                if(colors[i] == color){
                    sb.append((i + 1)).append(" ");
                    count++;
                    if(count == req){
                        break;
                    }
                }
            }
            sb.append("\n");
        }else {
            sb.append(2).append("\n");
            sb.append(cycle.size()).append("\n");
            for(int val : cycle){
                sb.append((val+1)).append(" ");
            }
            sb.append("\n");
        }
        System.out.print(sb.toString());
    }

    /** Faster input **/
    static class Reader {
        final private int BUFFER_SIZE = 1 << 32;private DataInputStream din;private byte[] buffer;private int bufferPointer, bytesRead;
        public Reader(){din=new DataInputStream(System.in);buffer=new byte[BUFFER_SIZE];bufferPointer=bytesRead=0;}
        public Reader(String file_name)throws IOException {din=new DataInputStream(new FileInputStream(file_name));buffer=new byte[BUFFER_SIZE];bufferPointer=bytesRead=0;}
        public String readLine()throws IOException{byte[] buf=new byte[1024*16];int cnt=0,c;
            while((c=read())!=-1){if(c=='\n')break;buf[cnt++]=(byte)c;}return new String(buf,0,cnt);}
        public int nextInt()throws IOException{int ret=0;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');
            if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(neg)return -ret;return ret;}
        public long nextLong()throws IOException{long ret=0;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');
            if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(neg)return -ret;return ret;}
        public double nextDouble()throws IOException{double ret=0,div=1;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c = read();do {ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');
            if(c=='.')while((c=read())>='0'&&c<='9')ret+=(c-'0')/(div*=10);if(neg)return -ret;return ret;}
        private void fillBuffer()throws IOException{bytesRead=din.read(buffer,bufferPointer=0,BUFFER_SIZE);if(bytesRead==-1)buffer[0]=-1;}
        private byte read()throws IOException{if(bufferPointer==bytesRead)fillBuffer();return buffer[bufferPointer++];}
        public void close()throws IOException{if(din==null) return;din.close();}
    }
}