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.util.*;
import java.io.*;
public class Main 
{
 
	static ArrayList<Integer> adj[];
	static char color[];
	static boolean b[],visited[],possible;
	static int level[];
	static Map<Integer,HashSet<Integer>> s;
	static int totalnodes,colored;
	static int count[];
	static long sum[];
	static double ans=0;
	static long[] as=new long[10001];
	static long c1=0,c2=0;
	public static void main(String[] args) throws IOException
	{
		in=new InputReader(System.in);
		w=new PrintWriter(System.out);
        int n=in.nextInt(),x=in.nextInt();
        if(n==2 && x==0)
           w.print("NO");
        else
        {
        	w.println("YES");
        	if(n==1)
        		w.print(x);
        	else if(n==2)
        		w.print(0+" "+x);
        	else
        	{
        		int y=0;
        		for(int i=1;i<=n-3;i++)
        			{
        			w.print(i+" ");
        			y=y^i;
        			}
        		long a=(long)Math.pow(2,17);
        		long b=(long)Math.pow(2, 18);
        		if(y==x)
        			w.print(a+" "+b+" "+(a+b));
        		else
        			w.print(b+" 0 "+(b^y^x));
        	}
        }
        
        
    w.close();
}
  public static void bfs()
  {
	 level[1]=1;
	 visited[1]=true;
	 Queue<Integer> q=new LinkedList<Integer>();
	 q.add(1);
	 while(!q.isEmpty())
	 {
		 int t=q.poll();
		 for(int i=0;i<adj[t].size();i++)
		 {
			 if(!visited[adj[t].get(i)])
			 {
				 level[adj[t].get(i)]=level[t]+1;
				 visited[adj[t].get(i)]=true;
				 q.add(adj[t].get(i));
			 }
		 }
	 }
  }
  public static void dfs(int i,int c)
  {
	  visited[i]=true;
	  if(c==0)
		  c1++;
	  else
		  c2++;
	  for(int j:adj[i])
	  {
		  if(!visited[j])
			  dfs(j,c^1);
	  }
	  
  }
	public static String rev(String s)
	{
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}
	static long lcm(long a, long b)
	{
	    return a * (b / gcd(a, b));
	}
	static long gcd(long a, long b)
	{
	    while (b > 0)
	    {
	        long temp = b;
	        b = a % b; // % is remainder
	        a = temp;
	    }
	    return a;
	}
	static InputReader in;
	static PrintWriter w;
static class InputReader 
{
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;
 
public InputReader(InputStream stream)
{
  this.stream = stream;
}
 
public int snext()
{
  if (snumChars == -1)
    throw new InputMismatchException();
  if (curChar >= snumChars)
  {
    curChar = 0;
    try 
    {
      snumChars = stream.read(buf);
    }
    catch (IOException e)
    {
      throw new InputMismatchException();
    }
    if (snumChars <= 0)
      return -1;
  }
  return buf[curChar++];
}
 
public int nextInt() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  int res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}
 
public long nextLong() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  long res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}
 
public int[] nextIntArray(int n) 
{
	 return nextIntArray(n, 0);
	    }
	    
public int[] nextIntArray(int n, int off)
{
	 int[] arr = new int[n + off];
	   for (int i = 0; i < n; i++)
	   {
	    arr[i + off] = nextInt();
	    }
	    return arr;
	    }
	    
public long[] nextLongArray(int n)
{
return nextLongArray(n, 0);
	    }
        
	public long[] nextLongArray(int n, int off)
	{
	 long[] arr = new long[n + off];
	 for (int i = 0; i < n; i++)
	 {
		  arr[i + off] = nextLong();
		 }
 return arr;
	}
 
 
public String readString() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isSpaceChar(c));
  return res.toString();
}
 
public String nextLine() 
{
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isEndOfLine(c));
  return res.toString();
}
 
public boolean isSpaceChar(int c)
{
  if (filter != null)
    return filter.isSpaceChar(c);
  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
 
private boolean isEndOfLine(int c) 
{
  return c == '\n' || c == '\r' || c == -1;
}
 
public interface SpaceCharFilter
{
  public boolean isSpaceChar(int ch);
}
}
	
}