Problem:
Score : 500 points

Problem Statement

You are given a connected undirected simple graph, which has N vertices and M edges.
The vertices are numbered 1 through N, and the edges are numbered 1 through M.
Edge i connects vertices A_i and B_i.
Your task is to find a path that satisfies the following conditions:

The path traverses two or more vertices.

The path does not traverse the same vertex more than once.

A vertex directly connected to at least one of the endpoints of the path, is always contained in the path.

It can be proved that such a path always exists.
Also, if there are more than one solution, any of them will be accepted.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i < B_i \leq N

The given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them).

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find one path that satisfies the conditions, and print it in the following format.
In the first line, print the count of the vertices contained in the path.
In the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path.

Sample Input 1

5 6
1 3
1 4
2 3
1 5
3 5
2 4

Sample Output 1

4
2 3 1 4

There are two vertices directly connected to vertex 2: vertices 3 and 4.
There are also two vertices directly connected to vertex 4: vertices 1 and 2.
Hence, the path 2 → 3 → 1 → 4 satisfies the conditions.

Sample Input 2

7 8
1 2
2 3
3 4
4 5
5 6
6 7
3 5
2 6

Sample Output 2

7
1 2 3 4 5 6 7

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.LinkedHashSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        agc013b solver = new agc013b();
        solver.solve(1, in, out);
        out.close();
    }

    static class agc013b {
        List[] g;
        boolean[] v;
        boolean isd = false;
        int ef = 0;
        LinkedHashSet<Integer> ans = new LinkedHashSet<>();
        Set<Integer> l = new HashSet<>();
        int le = -1;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();

            g = new List[n];

            for (int i = 0; i < n; i++) {
                g[i] = new ArrayList();
            }

            for (int i = 0; i < m; i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;

                g[a].add(b);
                g[b].add(a);
            }

            v = new boolean[n];

            dfs(0);

            v = new boolean[n];

            dfs2(le);

            v = new boolean[n];

            for (int num : ans) {
                v[num] = true;
            }

            int sz = 0;

            isd = false;
            dfs3(0);
            for (int num : ans) {
                sz++;
            }

            out.println(sz);
            for (int num : ans) {
                out.print((num + 1) + " ");
            }
        }

        void dfs2(int u) {
            if (isd)
                return;

            v[u] = true;
            ans.add(u);
            if (ans.contains(0)) {
                isd = true;
                return;
            }

            for (int ve : (List<Integer>) g[u]) {
                if (!v[ve]) {
                    dfs2(ve);
                }
            }

            if (!isd) {
                ans.remove(u);
            }
        }

        void dfs3(int u) {
            if (isd)
                return;

            v[u] = true;
            if (u != 0)
                ans.add(u);

            int c = 0;
            for (int ve : (List<Integer>) g[u]) {
                if (!v[ve]) {
                    c++;
                    dfs3(ve);
                }
            }

            if (c == 0) {
                isd = true;
                return;
            }
        }

        void dfs(int u) {
            v[u] = true;

            int c = 0;
            for (int ve : (List<Integer>) g[u]) {
                if (!v[ve]) {
                    c++;
                    if (u == 0) {
                        ef++;
                    }
                    dfs(ve);
                }
            }

            if (c == 0) {
                le = u;
                l.add(u);
            }
            if (g[u].size() == 1 && u == 0) {
                l.add(u);
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}