Problem: 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.

Examples

Input

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


Output

4
2 3 1 4


Input

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


Output

7
1 2 3 4 5 6 7

Solution (in JAVA):

Solution:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
    MyScanner      sc    = new MyScanner();
    Scanner        sc2   = new Scanner(System.in);
    long           start = System.currentTimeMillis();
    long           fin   = System.currentTimeMillis();
    final int      MOD   = 1000000007;
    int[]          dx    = { 1, 0, 0, -1 };
    int[]          dy    = { 0, 1, -1, 0 };

    int            N, M;
    boolean[]      v;
    Set<Integer>[] g;
    List<Integer>  p1;
    List<Integer>  p2;

    void run() {
        N = sc.nextInt();
        M = sc.nextInt();
        g = new HashSet[N];
        v = new boolean[N];
        for (int i = 0; i < N; i++) g[i] = new HashSet<>();
        for (int i = 0; i < M; i++) {
            int s = sc.nextInt() - 1;
            int t = sc.nextInt() - 1;
            g[s].add(t);
            g[t].add(s);
        }
        p1 = new ArrayList<>();
        p2 = new ArrayList<>();
        int ind = 0;
        for (int start : g[0]) {
            if (ind == 0) dfs(0);
            if (ind == 1) dfs2(-1 , 0);
            if (ind == 1)
                break;
            ind++;
        }

        List<Integer> l = new ArrayList<>();

        for (int i = 0; i < p2.size(); i++) l.add(p2.get(p2.size() - i - 1) + 1);
        l.add(1);
        for (int i = 0; i < p1.size(); i++) l.add(p1.get(i) + 1);
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < l.size(); i++) {
            if(i != 0) sb.append(" "+l.get(i));
            else sb.append(l.get(i));
        }
        System.out.println(l.size());
        System.out.println(sb);
    }

    void dfs(int now) {
        v[now] = true;
        for (int next : g[now]) {
            if (v[next]) continue;
            p1.add(next);
            dfs(next);
            return;
        }
    }

    void dfs2(int pre, int now) {
        v[now] = true;
        for (int next : g[now]) {
            if (v[next]) continue;
            p2.add(next);
            dfs2(now, next);
            return;
        }
    }

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

    void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    void debug2(int[][] array) {
        for (int i = 0; i < array.length; i++) {
            for (int j = 0; j < array[i].length; j++) {
                System.out.print(array[i][j]);
            }
            System.out.println();
        }
    }

    boolean inner(int h, int w, int limH, int limW) {
        return 0 <= h && h < limH && 0 <= w && w < limW;
    }

    void swap(char[] x, int a, int b) {
        char tmp = x[a];
        x[a] = x[b];
        x[b] = tmp;
    }

    // find minimum i (k <= a[i])
    int lower_bound(int a[], int k) {
        int l = -1;
        int r = a.length;
        while (r - l > 1) {
            int mid = (l + r) / 2;
            if (k <= a[mid])
                r = mid;
            else
                l = mid;
        }
        // r = l + 1
        return r;
    }

    // find minimum i (k < a[i])
    int upper_bound(int a[], int k) {
        int l = -1;
        int r = a.length;
        while (r - l > 1) {
            int mid = (l + r) / 2;
            if (k < a[mid])
                r = mid;
            else
                l = mid;
        }
        // r = l + 1
        return r;
    }

    int gcd(int a, int b) {
        return a % b == 0 ? b : gcd(b, a % b);
    }

    int lcm(int a, int b) {
        return a * b / gcd(a, b);
    }

    boolean palindrome(String s) {
        for (int i = 0; i < s.length() / 2; i++) {
            if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
                return false;
            }
        }
        return true;
    }

    class MyScanner {
        int nextInt() {
            try {
                int c = System.in.read();
                while (c != '-' && (c < '0' || '9' < c))
                    c = System.in.read();
                if (c == '-')
                    return -nextInt();
                int res = 0;
                do {
                    res *= 10;
                    res += c - '0';
                    c = System.in.read();
                } while ('0' <= c && c <= '9');
                return res;
            } catch (Exception e) {
                return -1;
            }
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

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

        String next() {
            try {
                StringBuilder res = new StringBuilder("");
                int c = System.in.read();
                while (Character.isWhitespace(c))
                    c = System.in.read();
                do {
                    res.append((char) c);
                } while (!Character.isWhitespace(c = System.in.read()));
                return res.toString();
            } catch (Exception e) {
                return null;
            }
        }

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

        int[][] nextInt2dArray(int n, int m) {
            int[][] in = new int[n][m];
            for (int i = 0; i < n; i++) {
                in[i] = nextIntArray(m);
            }
            return in;
        }

        double[] nextDoubleArray(int n) {
            double[] in = new double[n];
            for (int i = 0; i < n; i++) {
                in[i] = nextDouble();
            }
            return in;
        }

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

        char[][] nextCharField(int n, int m) {
            char[][] in = new char[n][m];
            for (int i = 0; i < n; i++) {
                String s = sc.next();
                for (int j = 0; j < m; j++) {
                    in[i][j] = s.charAt(j);
                }
            }
            return in;
        }
    }
}