You've got a undirected graph G, consisting of n nodes. We will consider the nodes of the graph indexed by integers from 1 to n. We know that each node of graph G is connected by edges with at least k other nodes of this graph. Your task is to find in the given graph a simple cycle of length of at least k + 1.

A simple cycle of length d (d > 1) in graph G is a sequence of distinct graph nodes v1, v2, ..., vd such, that nodes v1 and vd are connected by an edge of the graph, also for any integer i (1 ≤ i < d) nodes vi and vi + 1 are connected by an edge of the graph.

Input

The first line contains three integers n, m, k (3 ≤ n, m ≤ 105; 2 ≤ k ≤ n - 1) — the number of the nodes of the graph, the number of the graph's edges and the lower limit on the degree of the graph node. Next m lines contain pairs of integers. The i-th line contains integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the indexes of the graph nodes that are connected by the i-th edge. 

It is guaranteed that the given graph doesn't contain any multiple edges or self-loops. It is guaranteed that each node of the graph is connected by the edges with at least k other nodes of the graph.

Output

In the first line print integer r (r ≥ k + 1) — the length of the found cycle. In the next line print r distinct integers v1, v2, ..., vr (1 ≤ vi ≤ n) — the found simple cycle.

It is guaranteed that the answer exists. If there are multiple correct answers, you are allowed to print any of them.

Examples

Input

3 3 2
1 2
2 3
3 1


Output

3
1 2 3 

Input

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


Output

4
3 4 1 2 
import java.util.Scanner;
import java.io.OutputStream;
import java.io.IOException;
import java.util.Arrays;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.io.InputStream;

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

class TaskD {
    public void solve(int testNumber, Scanner in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        Vertex[] vertexes = new Vertex[n+1];
        for(int i = 0; i < n+1; ++i)
            vertexes[i] = new Vertex();

        for(int i = 0; i < m; ++i) {
            int from = in.nextInt();
            int to = in.nextInt();
            vertexes[from].edges.add(new Edge(from, to));
            vertexes[to].edges.add(new Edge(to, from));
        }

        boolean [] seen = new boolean[n+1];
        Arrays.fill(seen, false);
        seen[1] = true;
        int curr = 1;

        ArrayList<Integer> r = new ArrayList<Integer>();
        while (true) {
            r.add(curr);
            int next = -1;
            for(Edge e : vertexes[curr].edges) {
                if(seen[e.to])
                    continue;
                next = e.to;
                seen[e.to] = true;
                break;
            }

            if(next == -1)
                break;
            curr = next;
        }

        int[] finalNeigh = new int[n+1];
        for(Edge e : vertexes[curr].edges)
            finalNeigh[e.to] = 1;

        for(int i = 0; i < r.size(); ++i) {
            if(finalNeigh[r.get(i)] != 1)
                continue;

            out.println(r.size() - i);
            for(; i < r.size(); ++i)
                if(i != r.size()-1)
                    out.print(r.get(i) + " ");
                else
                    out.print(r.get(i) + "\n");
        }
    }



    private static class Vertex {
        public ArrayList<Edge> edges = new ArrayList<Edge>();

    }

    private static class Edge {
        public int from, to;

        private Edge(int from, int to) {
            this.from = from;
            this.to = to;
        }
    }


}

