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.util.*;
import java.io.*;

public class CFA {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000L * 1000L * 1000L + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    void solve() throws IOException {
        int T = 1;
        for (int i = 0; i < T; i++) {
            helper();
        }
    }

    int n;
    int m;
    int k;
    List<List<Integer>> graph = new ArrayList<>();
    boolean hasCycle = false;
    int[] color;
    int[] parent;
    int[] depth;
    int startPoint = -1;
    void helper() throws IOException {
        n = nextInt();
        m = nextInt();
        k = nextInt();
        for (int i = 0; i < n; i++) {
            graph.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int from = nextInt() - 1;
            int to = nextInt() - 1;
            graph.get(from).add(to);
            graph.get(to).add(from);
        }
        color = new int[n];
        Arrays.fill(color, -1);
        dfs(-1, 0, 0);
        if (!hasCycle) {
            int one = 0;
            for (int v : color) {
                if (v == 1) {
                    one++;
                }
            }
            int find = 2 * one >= n ? 1 : 0;
            List<Integer> res = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (color[i] == find) {
                    res.add(i);
                }
            }
            outln(1);
            int need = (k + 1) / 2;
            for (int i = 0; i < need; i++) {
                out((res.get(i) + 1) + " ");
            }
            outln("");
            return;
        }

        parent = new int[n];
        depth = new int[n];
        Arrays.fill(depth, Integer.MAX_VALUE);
        dfs2(-1, 0, 0);

        int start = startPoint;
        List<Integer> res = new ArrayList<>();
        while (true) {
            res.add(start);
            start = parent[start];
            if (start == startPoint) {
                break;
            }
        }

        if (res.size() <= k) {
            outln(2);
            outln(res.size());
            for (int v : res) {
                out((v + 1) + " ");
            }
            outln("");
            return;
        }

        outln(1);
        start = 0;
        int need = (k + 1) / 2;
        for (int i = 0; i < need; i++) {
            out((res.get(start) + 1) + " ");
            start += 2;
        }
        outln("");
    }

    boolean dfs2(int par, int cur, int d) {
        depth[cur] = d;
        parent[cur] = par;

        int deepest = -1;
        int point = -1;
        for (int nxt : graph.get(cur)) {
            if (nxt == par) {
                continue;
            }

            if (depth[nxt] != Integer.MAX_VALUE) {
                if (deepest < depth[nxt]) {
                    deepest = depth[nxt];
                    point = nxt;
                }
            }
        }
        if (deepest != -1) {
            startPoint = point;
            parent[point] = cur;
            return true;
        }

        for (int nxt : graph.get(cur)) {
            if (nxt == par) {
                continue;
            }
            if (dfs2(cur, nxt, d + 1)) {
                return true;
            }
        }

        return false;
    }

    void dfs(int par, int cur, int col) {
        if (color[cur] != -1) {
            hasCycle = true;
            return;
        }
        color[cur] = col;
        for (int nxt : graph.get(cur)) {
            if (nxt != par) {
                dfs(cur, nxt, 1 - col);
            }
        }
    }

    void shuffle(long[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            long tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        outln(String.format("%.9f%n", val));
    }
    public CFA() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFA();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}