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.util.* ;
public class Codeshefcode{
	public static void main(String[] args) throws IOException{
		Solver Machine = new Solver() ;
		Machine.Solve() ;
		Machine.Finish();
	}	
}
class Mod{
	static long mod=1000000007 ;
	static long d(long a,long b){ return (a*ModInverse(b))%mod ; }
	static long m(long a , long b){ return (a*b)%mod ; }
	static private long ModInverse(long a ){ return pow(a,mod-2) ; }
	static long pow(long a,long b){
		long val=a ; long ans=1 ;
		while(b!=0){
			if((b&1)==1) ans = m(ans,val) ; 
			val = m(val,val) ; 
			b>>=1 ;
		}
		return ans ;
	}	
}
class pair implements Comparable<pair>{
	int x ; int y ;
	pair(int a,int b){ x=a ; y=b ; }
	public int compareTo(pair p){
		return (this.x<p.x ? -1 : (this.x>p.x ? 1 : (this.y<p.y ? -1 : (this.y>p.y ? 1 : 0)))) ;
	}
}
class Solver{	
	FasterScanner ip = new FasterScanner(System.in) ;	  
	PrintWriter op = new PrintWriter(System.out) ;
	void Solve() throws IOException{
		int n = ip.i() ;
		int x = ip.i() ;
		if(n==2 && x==0){
			pln("NO") ;
			return ;
		}
		int nq = (n/4)*4 ;
		int k = n%4 ;
		mylist ls = new mylist() ;
		for(int i=0 ; i<nq ; i++) ls.add(100004+i) ;
		if(x==0){
			switch(k){
				case 0:{
				}break ;
				case 1:{
					addElem(ls,0) ;
				}break ;
				case 2:{
					for(int i=0 ; i<4 ; i++)
						ls.remove(ls.size()-1) ;
					addElem(ls,1,2,3,4,8,12) ;
				}break ;
				case 3:{
					addElem(ls,1,2,3) ;
				}break ;
			}
		}else{
			if(k==0){ 
				k+=4 ;
				for(int i=0 ; i<4 ; i++)
					ls.remove(ls.size()-1) ;					
			}
			switch(k){
				case 1:{
					addElem(ls,x) ;
				}break ;
				case 2:{
					addElem(ls,0,x) ;
				}break ;
				case 3:{
					addElem(ls,0) ;
					if(x==1) addElem(ls,2,3) ;
					else
						addElem(ls,1,1^x) ;
				}break ;
				case 4:{
					if(x>3)
						addElem(ls,x,1,2,3) ;
					else 
						addElem(ls,x,4,8,12) ;
				}
			}
		}
		pln("YES") ;
		pls(ls) ;		
	}
	void addElem(mylist ls,Integer... args){
		for(int elem : args)
			ls.add(elem) ;
	}
	void pls(mylist ls){
		for(int elem : ls) p(elem+" ") ;
	}
	void p(Object o){
		op.print(o) ;
	}
	void pln(Object o){
		op.println(o) ;
	}
	void Finish(){
		op.flush();
		op.close();
	}	
}
@SuppressWarnings("serial")
class mylist extends ArrayList<Integer>{
}
@SuppressWarnings("serial")
class myset extends TreeSet<Integer>{
	
}
@SuppressWarnings("serial")
class mystack extends Stack<pair>{
	
}
class FasterScanner { 
	private InputStream mIs;
	private byte[] buf = new byte[1024];
	private int curChar,numChars;
	public FasterScanner() { this(System.in); } 
	public FasterScanner(InputStream is) { mIs = is;} 
	public int read() {
		if (numChars == -1) throw new InputMismatchException();    
		if (curChar >= numChars) {
			curChar = 0;
			try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}
			if (numChars <= 0) return -1;            
		}
		return buf[curChar++];
	} 
	public String nextLine(){
		int c = read();
		while (isSpaceChar(c)) c = read();        
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	} 
	public String S(){
		int c = read();
		while (isSpaceChar(c)) c = read();        
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		}while (!isSpaceChar(c));
		return res.toString();
	} 
	public long l(){
		int c = read();
		while (isSpaceChar(c)) c = read();        
		int sgn = 1;
		if (c == '-') { sgn = -1 ; c = read() ; }
		long res = 0;
		do{
			if (c < '0' || c > '9') throw new InputMismatchException();
			res *= 10 ; res += c - '0' ; c = read();
		}while(!isSpaceChar(c));
		return res * sgn;
	} 
	public int i(){
		int c = read() ;
		while (isSpaceChar(c)) c = read();        
		int sgn = 1;
		if (c == '-') { sgn = -1 ; c = read() ; }
		int res = 0;
		do{
			if (c < '0' || c > '9') throw new InputMismatchException();
		res *= 10 ; res += c - '0' ; c = read() ;
		}while(!isSpaceChar(c));
		return res * sgn;
	} 
	public int[] ia(int n){
		int a[] = new int[n] ;
		for(int i=0 ; i<n ; i++) a[i] = i() ;
		return a ;
	}
	public long[] la(int n){
		long a[] = new long[n] ;
		for(int i=0 ; i<n ; i++) a[i] = l() ;
		return a ;
	}
	public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
	public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
}