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

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        while(true) {
            int N = sc.nextInt();
            int M = sc.nextInt();

            if( N == 0 ) break;

            int[] A = new int[M];
            int[] B = new int[M];
            for (int i = 0; i < M; i++) {
                A[i] = sc.nextInt()-1;
                B[i] = sc.nextInt()-1;
            }
            int[] ans = solve(N, M, A, B);
            out.println(ans.length);
            for (int a : ans) {
                out.println(a);
            }
        }
        out.flush();
    }

    static int[] solve(int N, int M, int[] A, int[] B) {
        int[][] G = adjB(N, A, B);
        int[] parity = new int[N];
        Arrays.fill(parity, -1);
        boolean ok = dfs(0, true, G, parity);
        if( ok ) {

            int on = 0;
            int off = 0;
            for (int i = 0; i < N; i++) {
                if( parity[i] == 1 ) {
                    on++;
                } else {
                    off++;
                }
            }

            Set<Integer> set = new HashSet<>();
            if( on % 2 == 0 ) set.add(on/2);
            if( off % 2 == 0 ) set.add(off/2);

            int[] ans = new int[set.size()];
            int idx = 0;
            for (Integer a : set) {
                ans[idx++] = a;
            }
            Arrays.sort(ans);
            return ans;

        } else {
            return new int[0];
        }
    }

    static boolean dfs(int a, boolean p, int[][] G, int[] parity) {
        if( parity[a] != -1 ) {
            int exp = p ? 1 : 0;
            int act = parity[a];
            return exp == act;
        }

        parity[a] = p ? 1 : 0;
        for (int b : G[a]) {
            boolean ok = dfs(b, !p, G, parity);
            if( !ok ) return false;
        }
        return true;
    }

    static int[][] adjB(int n, int[] from, int[] to) {
        int[][] adj = new int[n][];
        int[] cnt = new int[n];
        for (int f : from) {
            cnt[f]++;
        }
        for (int t : to) {
            cnt[t]++;
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new int[cnt[i]];
        }
        for (int i = 0; i < from.length; i++) {
            adj[from[i]][--cnt[from[i]]] = to[i];
            adj[to[i]][--cnt[to[i]]] = from[i];
        }
        return adj;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

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

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

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

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < array.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(array[i]);
        }
        pw.println();
        pw.flush();
    }

    static int lowerBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] < value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }

    static int upperBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] <= value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }
}



Measured memory_bytes: 40532