package contest200911; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.InputMismatchException; import java.util.List; public class F { InputStream is; PrintWriter out; String INPUT = ""; void solve() { //// int[] q = new int[]{1, 1, 2, 2, 3}; // int[] q = new int[]{3}; // int u = q.length; // int ct = 0; // int[] t = new int[16]; // for(int i = 0;i < 1< 0 ? 1 : 0;;need++){ long got = (1L<= M){ List span = new ArrayList<>(); span.add(K); int h = 1; while(basis(span) < need){ span.add(h); h *= 2; } M += need; int OM = M; List ret = new ArrayList<>(); long[] bas = basis2(span); if(M > 0){ ret.add(K); M--; } if(M > 0){ ret.add(K); M--; } for(int i = 0;i < 1<<20 && M > 0;i++){ if(i == K)continue; if(M > 0 && hasSolution(i, bas)){ ret.add(i); M--; } if(M > 0 && hasSolution(i, bas)){ ret.add(i); M--; } } out.println("Yes"); out.println(OM); for(int v : ret){ out.print(v + " "); } out.println(); return; } } } public static long basis(List span) { long[] bas = new long[64]; for(long x : span){ int h = 63-Long.numberOfLeadingZeros(x); while(x != 0){ if(bas[h] != 0){ x ^= bas[h]; h = 63-Long.numberOfLeadingZeros(x); }else{ bas[h] = x; } } } long ret = 0; for(int i = 0;i <64;i++){ if(bas[i] != 0){ ret++; } } return ret; } public static boolean hasSolution(long x, long[] bas) { int h = 63-Long.numberOfLeadingZeros(x); while(x != 0){ if(bas[h] != 0){ x ^= bas[h]; h = 63-Long.numberOfLeadingZeros(x); }else{ return false; } } return true; } public static long[] basis2(List span) { long[] bas = new long[64]; for(long x : span){ int h = 63-Long.numberOfLeadingZeros(x); while(x != 0){ if(bas[h] != 0){ x ^= bas[h]; h = 63-Long.numberOfLeadingZeros(x); }else{ bas[h] = x; } } } return bas; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new F().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }