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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;
import java.math.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration

    static class pair implements Comparable < pair > {
        int x;
        int y;


        pair(int i, int j) {
            x = i;
            y = j;


        }
        public int compareTo(pair p) {
            if (this.x != p.x) {
                return this.x - p.x;
            } else {
                return this.y - p.y;
            }
        }
        public int hashCode() {
            return (x + " " + y).hashCode();
        }
        public String toString() {
            return x + " " + y;
        }
        public boolean equals(Object o) {
            pair x = (pair) o;
            return (x.x == this.x && x.y == this.y);
        }
    }
    // int[] dx = {0,0,1,-1};
    // int[] dy = {1,-1,0,0};
    // int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
    // int[] ddy = {1,-1,0,0,1,-1,-1,1};

int inf = (int) 1e9 + 5;
long mod = (long)1e9 + 7 ;  
ArrayList<ArrayList<Integer>> g ;
int n,m,k;
int[] par,dist;
boolean[] vis ;
boolean done = false ;
int smallest_cycle = inf ;
void solve() throws Exception {
     n=ni();m=ni();k=ni();
    g= ng(n,m);
   // pn("graph "+g);
    par = new int[n+1];
    dist = new int[n+1];
    vis = new boolean[n+1];
    if(m==n-1){
        pn(1);
        int[] col = bfs(1);
        ArrayList<Integer> w = new ArrayList<>();
        ArrayList<Integer> b = new ArrayList<>();
       
        for(int i=1;i<=n;++i){
            if(col[i]==0) w.add(i);
            else b.add(i);
        }
        if(w.size()>b.size()){
            
            for(int i=0;i<(k+1)/2;++i) p(w.get(i)+" ");
            
            pn("");
        }
        else{
            
            for(int i=0;i<(k+1)/2;++i) p(b.get(i)+" ");
            pn("");
        }
        
    }
    else{
        small_cycle_dfs(1,1,0);
       // pn("smallest cycle "+smallest_cycle);
        vis = new boolean[n+1];
        dist =new int[n+1];
        par = new int[n+1];
        dfs(1,1,0);

    }
} 
void small_cycle_dfs(int s,int p,int d){
   //pn("visiting "+s+" par "+p);
    if(vis[s]){
        if(d-dist[s]>0)
        smallest_cycle = Math.min(d-dist[s],smallest_cycle);
        //pn("small cycle "+smallest_cycle);
    }
    else{
        vis[s]  = true ;
        dist[s] =  d ;
        par[s]  = p ;
        for(int x: g.get(s)){
            if(x==p) continue;
            small_cycle_dfs(x,s,d+1);
        }
    }
}
void dfs(int s,int p,int d){
    if(vis[s]){
       // pn("visited "+s);
        if(!done &&( d-dist[s]==smallest_cycle)){
            done = true ;
        ArrayList<Integer> ans = new ArrayList<>();
       // print("par array "+Arrays.toString(par));
        while(p != s){
            ans.add(p);
            p = par[p];
        }
        ans.add(s);

        if(d - dist[s] <=k){
            
            pn(2);
            pn(ans.size());
            for(int x: ans){
                p(x+" ");
            }

            pn("");
            
        }
        else{
            pn(1);
            int cnt = 0; 
            for(int i=0;i<ans.size()&& cnt < (k+1)/2;i+=2){
                p(ans.get(i)+" ");
                cnt++ ;
            }
            pn("");
        }
    }

        
    }
    else{
       // pn("visited "+s);
        vis[s]  = true ;
        dist[s] =  d ;
        par[s]  = p ;
        for(int x: g.get(s)){
            if(x==p) continue;
            dfs(x,s,d+1);
        }
    }
    
}
int[] bfs(int s){
	LinkedList<pair> q = new LinkedList<>();
	boolean[] vis= new boolean[g.size()];
	int[] dis = new int[g.size()];
	q.add(new pair(s,0));
	dis[0] = -1; 
	while(!q.isEmpty()){
		pair p = q.pollFirst();
		if(vis[p.x]) continue ;
		vis[p.x] = true ;
		dis[p.x] = dis[p.y] +1 ;

		for(int x:g.get(p.x)){
			q.add(new pair(x,p.x));
		}
    }
    for(int i=1;i<g.size();++i){
        dis[i] =dis[i]%2;
    }
    return dis;
}

  
    long pow(long a, long b) {
        long result = 1;
        while (b > 0) {
            if (b % 2 == 1) result = (result * a) % mod;
            b /= 2;
            a = (a * a) % mod;
        }
        return result;
    }


    void print(Object o) {
        System.out.println(o);
        System.out.flush();
    }



    long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
    }


    public static void main(String[] args) throws Exception {
        new Main().run();
    }

    //output methods
    private void pn(Object o) {
        out.println(o);
    }
    private void p(Object o) {
        out.print(o);
    }
    private ArrayList < ArrayList < Integer >> ng(int n, int e) {
        ArrayList < ArrayList < Integer >> g = new ArrayList < > ();
        for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());

        for (int i = 0; i < e; ++i) {
            int u = ni(), v = ni();
            g.get(u).add(v);
            g.get(v).add(u);
        }

        return g;
    }

    private ArrayList < ArrayList < pair >> nwg(int n, int e) {
        ArrayList < ArrayList < pair >> g = new ArrayList < > ();
        for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());

        for (int i = 0; i < e; ++i) {
            int u = ni(), v = ni(), w = ni();
            g.get(u).add(new pair(w, v));
            g.get(v).add(new pair(w, u));
        }

        return g;
    }


    //input methods
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;


    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }




    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }
    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private void tr(Object...o) {
        if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
    }
    void watch(Object...a) throws Exception {
        int i = 1;
        print("watch starts :");
        for (Object o: a) {
            //print(o);
            boolean notfound = true;
            if (o.getClass().isArray()) {

                String type = o.getClass().getName().toString();
                //print("type is "+type);
                switch (type) {
                    case "[I":
                        {
                            int[] test = (int[]) o;
                            print(i + " " + Arrays.toString(test));
                            break;
                        }
                    case "[[I":
                        {
                            int[][] obj = (int[][]) o;

                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[J":
                        {

                            long[] obj = (long[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[J":
                        {

                            long[][] obj = (long[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[D":
                        {

                            double[] obj = (double[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[D":
                        {

                            double[][] obj = (double[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[Ljava.lang.String":
                        {

                            String[] obj = (String[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[Ljava.lang.String":
                        {

                            String[][] obj = (String[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[C":
                        {
                            char[] obj = (char[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[C":
                        {

                            char[][] obj = (char[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }



                    default:
                        {
                            print(i + " type not identified");
                            break;
                        }
                }
                notfound = false;

            }
            if (o.getClass() == ArrayList.class) {
                print(i + " al: " + o);
                notfound = false;
            }
            if (o.getClass() == HashSet.class) {
                print(i + " hs: " + o);
                notfound = false;
            }
            if (o.getClass() == TreeSet.class) {
                print(i + " ts: " + o);
                notfound = false;
            }
            if (o.getClass() == TreeMap.class) {
                print(i + " tm: " + o);
                notfound = false;
            }
            if (o.getClass() == HashMap.class) {
                print(i + " hm: " + o);
                notfound = false;
            }
            if (o.getClass() == LinkedList.class) {
                print(i + " ll: " + o);
                notfound = false;
            }
            if (o.getClass() == PriorityQueue.class) {
                print(i + " pq : " + o);
                notfound = false;
            }
            if (o.getClass() == pair.class) {
                print(i + " pq : " + o);
                notfound = false;
            }

            if (notfound) {
                print(i + " unknown: " + o);
            }
            i++;
        }
        print("watch ends ");
    }

}