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.*;
import java.lang.Math.*;

public class MainA
{

	static int mod = (int) 1e9 + 7;

	public static void main(String[] args) throws java.lang.Exception
	{
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n=in.nextInt();
		int x=in.nextInt();
		int re=n%4;
		if(re==0)re=4;
		
		
		
		int lastbit=x%2;
		int second_lastbit=0;
		if(x%4==2 ||x%4==3)
		{
			second_lastbit=1;
		}
		int arr[]=new int[4];
		int type=-1;
		if(lastbit==0)
		{
			if(second_lastbit==0)
			{
				type=1;
				arr[0]=x;arr[1]=x+1;arr[2]=x+2;arr[3]=x+3;
			}
			else
			{
				type=2;
				arr[0]=x-2;arr[1]=x-1;arr[2]=x;arr[3]=x+1;
			}
		}
		else
		{
			if(second_lastbit==0)
			{
				type=3;
				arr[0]=x-1;arr[1]=x;arr[2]=x+1;arr[3]=x+2;
			}
			else
			{
				type=4;
				arr[0]=x-3;arr[1]=x-2;arr[2]=x-1;arr[3]=x;
			}
		}
		if(re==2)
		{
			if(x!=0)
			{
				out.println("YES");
				out.print(x+" "+"0"+" ");
				int count=n-re;
				
				for(int i=20;;i++)
				{
					if(count<=0)break;
					if(i!=arr[0] && i!=arr[1] && i!=arr[2] && i!=arr[3] )
					{
						out.print(i+" ");
						count--;
					}
				}
			}
			else
			{
				if(n==2)
				{
					out.println("NO");
				}
				else
				{
					out.println("YES");
					out.print(0+" "+2+" "+3+" "+5+" "+8+" "+12+" ");
					int count=n-6;
					for(int i=20;;i++)
					{
						if(count<=0)break;
						
							out.print(i+" ");
							count--;
						
					}
				}
			}
			out.close();
			return;
		}
		
		
		out.println("YES");
		if(re==1)
		{
			out.print(x+" ");
		}		
		else if(re==3 && x<=3)
		{
			if(x==0)
			{
				out.print(1+" "+2+" "+3+" ");
			}
			if(x==1)
			{
				out.print(0+" "+2+" "+3+" ");
			}
			if(x==2)
			{
				out.print(0+" "+1+" "+3+" ");
			}
			if(x==3)
			{
				out.print(0+" "+1+" "+2+" ");
			}
		}
		else if(re==3)
		{
			if(type==1)
			{
				out.print(x+1+" "+"1"+" "+"0"+" ");
			}
			else if(type==2)
			{
				out.print(x+1+" "+"1"+" "+"0"+" ");
			}
			else if(type==3)
			{
				out.print(x+2+" "+"2"+" "+"0"+" ");
			}
			else
			{
				out.print(x-1+" "+"1"+" "+"0"+" ");
			}
		}
		else if(re==4)
		{
			if(x>3||x==0 )
			out.print(x+" "+1+" "+2+" "+3+" " );
			else
			{
				if(x==1)
				{
					out.print(x+" "+6+" "+8+" "+14+" ");
				}
				else if(x==2)
				{
					out.print(1+" "+2+" "+6+" "+7+" ");
				}
				else
				{
					out.print(1+" "+3+" "+4+" "+5+" ");
				}
			}
		}
		int count=n-re;
		
		for(int i=20;;i++)
		{
			if(count<=0)break;
			if(i!=arr[0] && i!=arr[1] && i!=arr[2] && i!=arr[3] )
			{
				out.print(i+" ");
				count--;
			}
		}
		out.close();
	}

	static class Pairs implements Comparable<Pairs>
	{
		int x;
		int y;
		int z;
		
		Pairs(int a, int b,int c)
		{
			x = a;
			y = b;
			z=c;
		}

		@Override
		public int compareTo(Pairs o)
		{
			// TODO Auto-generated method stub
			if (y == o.y)
			{	
				if(z!=o.z)
				return Integer.compare(-z, -o.z);
				else
				return Integer.compare(x,o.x);	
			}	
			else
				return Integer.compare(y, o.y);
		}

	}

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

	public static boolean isPal(String s) 
	{
		for (int i = 0, j = s.length() - 1; i <= j; i++, j--)
		{
			if (s.charAt(i) != s.charAt(j))
				return false;
		}
		return true;
	}

	public static String rev(String s)
	{
		StringBuilder sb = new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}

	public static long gcd(long x, long y)
	{
		if (y == 0)
			return x;
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static int gcd(int x, int y)
	{
		if(y==0)
			return x;
		if (x % y == 0)
			return y;
		else
			return gcd(y, x % y);
	}

	public static long gcdExtended(long a, long b, long[] x) 
	{

		if (a == 0) 
		{
			x[0] = 0;
			x[1] = 1;
			return b;
		}
		long[] y = new long[2];
		long gcd = gcdExtended(b % a, a, y);

		x[0] = y[1] - (b / a) * y[0];
		x[1] = y[0];

		return gcd;
	}

	
	

	public static long max(long a, long b) 
	{
		if (a > b)
			return a;
		else
			return b;
	}

	public static long min(long a, long b)
	{
		if (a > b)
			return b;
		else
			return a;
	}

	public static long[][] mul(long a[][], long b[][])
	{
		long c[][] = new long[2][2];
		c[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0];
		c[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1];
		c[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0];
		c[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1];

		return c;
	}

	public static long[][] pow(long n[][], long p, long m)
	{
		long result[][] = new long[2][2];
		result[0][0] = 1;
		result[0][1] = 0;
		result[1][0] = 0;
		result[1][1] = 1;

		if (p == 0)
			return result;
		if (p == 1)
			return n;
		while (p != 0)
		{
			if (p % 2 == 1)
				result = mul(result, n);
			//System.out.println(result[0][0]);
			for (int i = 0; i < 2; i++)
			{
				for (int j = 0; j < 2; j++)
				{
					if (result[i][j] >= m)
						result[i][j] %= m;
				}
			}

			p >>= 1;
			n = mul(n, n);
			// System.out.println(1+" "+n[0][0]+" "+n[0][1]+" "+n[1][0]+" "+n[1][1]);
			for (int i = 0; i < 2; i++) 
			{
				for (int j = 0; j < 2; j++)
				{
					if (n[i][j] >= m)
						n[i][j] %= m;
				}
			}
		}
		return result;
	}
	public static long pow(long n,long p, long m)
	{
		long result=1;
		if(p==0)return 1;
		if(p==1)return n%m;
		while(p!=0)
		{
			if(p%2==1)result=(result*n)%m;
			p >>=1;
			n=(n*n)%m;
		}
		return result;
	}
	public static long pow(long n, long p) 
	{
		long result = 1;
		if (p == 0)
			return 1;
		if (p == 1)
			return n;
		while (p != 0)
		{
			if (p % 2 == 1)
				result *= n;
			p >>= 1;
			n *= n;
		}
		return result;
	}

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

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

		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);
		}
	}
}