Problem: Mahmoud and Ehab are on the third stage of their adventures now. As you know, Dr. Evil likes sets. This time he won't show them any set from his large collection, but will ask them to create a new set to replenish his beautiful collection of sets.

Dr. Evil has his favorite evil integer x. He asks Mahmoud and Ehab to find a set of n distinct non-negative integers such the bitwise-xor sum of the integers in it is exactly x. Dr. Evil doesn't like big numbers, so any number in the set shouldn't be greater than 106.

Input

The only line contains two integers n and x (1 ≤ n ≤ 105, 0 ≤ x ≤ 105) — the number of elements in the set and the desired bitwise-xor, respectively.

Output

If there is no such set, print "NO" (without quotes).

Otherwise, on the first line print "YES" (without quotes) and on the second line print n distinct integers, denoting the elements in the set is any order. If there are multiple solutions you can print any of them.

Examples

Input

5 5


Output

YES
1 2 4 5 7

Input

3 6


Output

YES
1 2 5

Note

You can read more about the bitwise-xor operation here: <https://en.wikipedia.org/wiki/Bitwise_operation#XOR>

For the first sample <image>.

For the second sample <image>.

Solution (in JAVA):

Solution:
	import java.io.*;



import java.math.*;
import java.nio.file.attribute.AclEntry.Builder;
import java.security.KeyStore.Entry;
import java.util.*;


	 
	public  class Khatri {
		private InputStream is;
		private PrintWriter out;
		int time = 0, DP[], start[], end[], dist[],  black[];
		static int MOD = (int)(1e9+7);
		int arr[];
		int weight[][];
		int x[];
		int y[];
		int parent[];
		int MAX = 800000, N, K, L;
		long red[];
		ArrayList<Integer>[] amp;
		HashSet<Integer> hs = new HashSet<>();
		long Dp[][][][] = new long[110][110][12][12];
		public static void main(String[] args) throws Exception 
		{
			new Thread(null, new Runnable() 
			{
			public void run() 
			{
				try {
	 
			//new CODEFORCES().soln();
			} catch (Exception e) 
				{
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
			new Khatri().soln();
		}
		char ch[][]; 
		int n1, n2, k1, k2, M;
		static ArrayList<Integer>[] g;
        static ArrayList<Integer> ar[];
		static long ok[];	 
		static int phi[]=new int[500005];
		void solve()
        {
			int xor=0;
			int tmp=-1;
			for(int i=1;i<=1000000;i++)
			{
				xor^=i;
				if(xor==0)
				{
					tmp=i;
				}
			}
			int n=ni();
			int x=ni();
			if(n==2&&x==0)
			{
				out.print("NO");
				return;
			}
			out.println("YES");
			if(x==0&&n%4==2)
			{
				n-=3;
				out.print(1+" "+2+" "+3+" ");
				
			}
			if(n==3)
			{
				if(x==0)
				{
					out.print(12+" "+4+" "+8);
					return;
				}
			}
			if(n%4==0)
			{
				if(x==0)
				{
					for(int i=tmp;i>=0;i--)
					{
						if(n>0)
						{
							out.print(i+" ");
						}
						else
							break;
						n--;
					}
					return;
				}
				else
				{
					n-=4;
					for(int i=tmp;i>=0;i--)
					{
						if(n>0)
						{
							out.print(i+" ");
						}
						else
							break;
						n--;
					}
					if(x>4)
				    out.print(1+" "+2+" "+3+" "+x);	
					else
						out.print(4+" "+8+" "+12+" "+x);
				}
			}
			else if(n%4==1)
			{
				n--;
				for(int i=tmp;i>=0;i--)
				{
					if(n>0)
					{
						out.print(i+" ");
					}
					else
						break;
					n--;
				}
				out.print(x);
				return;
			}
			else if(n%4==2)
			{
				n-=2;
				for(int i=tmp;i>=0;i--)
				{
					if(n>0)
					{
						out.print(i+" ");
					}
					else
						break;
					n--;
				}
				out.print(0+" "+x);
				return;
			}
			else if(n%4==3)
			{
				n-=3;
				for(int i=tmp;i>=0;i--)
				{
					if(n>0)
					{
						out.print(i+" ");
					}
					else
						break;
					n--;
				}
				
				for(int i=0;i<=100000;i++)
				{
					
					int p=i^(i+1)^(i+2)^(i+3);
					if(p==0)
					{
						if(i==x)
						{
							out.print((i+1)+" "+(i+2)+" "+(i+3));
							return;
						}
						if(i+1==x)
						{
							out.print((i)+" "+(i+2)+" "+(i+3));
							return;
						}   
						if(i+2==x)
						{
							out.print((i+1)+" "+(i)+" "+(i+3));
							return;
						}
						if(i+3==x)
						{
							out.print((i)+" "+(i+2)+" "+(i+1));
							return;
						}
					}
				}
			}
        } 
	
		
			
        
		
		
	    
		
              
       

       
       
            boolean isPrime(int x)
            {
            if(x==0||x==1)
            	return false;
			for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
			return true;
		}
	    int  p ;
		void buildGraph(int n)
		{
			for(int i = 0; i<n ;i++){
				int x1 = ni() -1, y1 = ni()-1;
				amp[x1].add(y1);
				amp[y1].add(x1);
				x[i] = x1; y[i] = y1;
			}
		}
		long get(int x){
			long val = 0;
			for(int i = 0; i< N; i++){
				val += Math.abs(x-arr[i]);
				x+=L;
			}
			return val;
		}
		
		long modInverse(long a, long mOD2){
	        return  power(a, mOD2-2, mOD2);
		}
		long power(long x, long y, long m)
		{
			if (y == 0)
	    return 1;
		long p = power(x, y/2, m) % m;
		p = (p * p) % m;
	 
		return (y%2 == 0)? p : (x * p) % m;
		}
		
		public static long gcd(long a, long b){
			if(b==0) return a;
			return gcd(b,a%b);
		}
		
		public static int[] shuffle(int[] a, Random gen){
			for(int i = 0, n = a.length;i < n;i++)
			{ 
				int ind = gen.nextInt(n-i)+i; 
				int d = a[i]; 
				a[i] = a[ind];
				a[ind] = d; 
			} 
		return a; 
		}
	 
		
		class Pair1 implements Comparable<Pair1>{
			String s;
			int val;
			Pair1(String s,int time){
			this.s=s;
			this.val=time;
			}
			public int hashCode() {
				return Objects.hash();
			}
			
			@Override
			public int compareTo(Pair1 arg0) {
				return (int)(arg0.val-val);
			}
			
		}
		long power(long x, long y, int mod){
			long ans = 1;
			while(y>0){
				if(y%2==0){
					x = (x*x)%mod;
					y/=2;
				}
				else{
					ans = (x*ans)%mod;
					y--;
				}
			}
			return ans;
		}
		void soln() {
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
            out.flush();
		}
 		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))) { 
				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[][] nm(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++)
			{
				for(int j=0;j<m;j++)
					map[i][j]=ni();
			}
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() {
			int num = 0, 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 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 boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	 
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}