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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Random;
import java.util.StringTokenizer;

public final class D {

    private static final class UnionFind {
        private final int[] parent;
        private final int[] size;
        private int count;

        private UnionFind(int n) {
            parent = new int[n];
            size = new int[n];
            count = n;
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                size[i] = 1;
            }
        }

        public int find(int p) {
            // path compression
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];
                p = parent[p];
            }
            return p;
        }

        public void union(int p, int q) {
            final int rootP = find(p);
            final int rootQ = find(q);
            if (rootP == rootQ) {
                return;
            }
            // union by size
            if (size[rootP] > size[rootQ]) {
                parent[rootQ] = rootP;
                size[rootP] += size[rootQ];
            } else {
                parent[rootP] = rootQ;
                size[rootQ] += size[rootP];
            }
            count--;
        }

        public int count() { return count; }

        public int[] size() { return size; }
    }

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        final int m = fs.nextInt();
        final int k = fs.nextInt();
        final UnionFind uf = new UnionFind(k);
        final Map<Integer, List<Integer>> g = new HashMap<>();
        int first = -1;
        int last = -1;
        boolean cycle = false;
        for (int i = 0; i < m; i++) {
            final int u = fs.nextInt() - 1;
            final int v = fs.nextInt() - 1;
            if (u < k && v < k) {
                g.computeIfAbsent(u, val -> new ArrayList<>()).add(v);
                g.computeIfAbsent(v, val -> new ArrayList<>()).add(u);
                if (uf.find(u) == uf.find(v)) {
                    cycle = true;
                    first = u;
                    last = v;
                    break;
                } else {
                    uf.union(u, v);
                }
            }
        }
        if (cycle) {
            final boolean[] seen = new boolean[k];
            final int[] par = new int[k];
            dfs1(first, -1, seen, par, g);
            par[first] = last;
            final List<Integer> res = new ArrayList<>();
            while (last != first) {
                res.add(last);
                last = par[last];
            }
            res.add(last);
            System.out.println(2);
            System.out.println(res.size());
            printList(res);
        } else {
            final List<Integer> even = new ArrayList<>();
            final List<Integer> odd = new ArrayList<>();
            final boolean[] seen = new boolean[k];
            for (int i = 0; i < k; i++) {
                dfs2(i, seen, g, even, odd, 0);
            }
            final List<Integer> res = even.size() > odd.size() ? even : odd;
            System.out.println(1);
            printList(res.subList(0, (k + 1) / 2));
        }
    }

    private static void printList(List<Integer> res) {
        for (int num : res) {
            System.out.print((num + 1) + " ");
        }
        System.out.println();
    }

    private static void dfs1(int curr, int par, boolean[] seen, int[] parents, Map<Integer, List<Integer>> g) {
        if (seen[curr]) {
            return;
        }
        parents[curr] = par;
        seen[curr] = true;
        for (int next : g.getOrDefault(curr, Collections.emptyList())) {
            if (next != par) {
                dfs1(next, curr, seen, parents, g);
            }
        }
    }

    private static void dfs2(int curr, boolean[] seen, Map<Integer, List<Integer>> g,
                             List<Integer> even, List<Integer> odd, int d) {
        if (seen[curr]) {
            return;
        }
        if (d % 2 == 0) {
            even.add(curr);
        } else {
            odd.add(curr);
        }
        seen[curr] = true;
        for (int next : g.getOrDefault(curr, Collections.emptyList())) {
            dfs2(next, seen, g, even, odd, d + 1);
        }
    }

    static final class Utils {
        public static void shuffleSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffleSort(long[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffle(int[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void shuffle(long[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void swap(int[] x, int i, int j) {
            final int t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        public static void swap(long[] x, int i, int j) {
            final long t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        private Utils() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        int[] nextIntArray(int n) {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++) { a[i] = nextInt(); }
            return a;
        }

        long[] nextLongArray(int n) {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++) { a[i] = nextLong(); }
            return a;
        }
    }
}