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 main
{
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	//private static long mod = 1000000000 + 7;
	private static long mod=100000000;
	private static long mod1 = 1000000000 + 9;
	private static void soln()
	{
		int n=nextInt();
		int x=nextInt();
		if(n==2 && x==0)
			pw.println("NO");
		else {
			pw.println("YES");
			if(n==1)
				pw.println(x);
			if(n==2)
				pw.println(1+" "+(1^x));
			else if(n>2){
				if(n==3 && x==0) {
					pw.println(1+" "+2+" "+3);
				}else {
					int xor=0;
					for(int i=1;i<=n-2;i++) {
						xor^=i;
					}
					//System.out.println(x^xor);
					int find=x^xor;
					if(find!=0) {
						for(int i=1;i<=n-2;i++) {
							pw.print(i+" ");
						}
						for(int i=n-1;i<=1000000;i++) {
							int x1=find^i;
							if(x1>n-2 && x1!=i) {
								pw.println(i+" "+x1);
								break;
							}
						}
					}else {
						find^=(n-2);
						for(int i=1;i<=n-3;i++) {
							pw.print(i+" ");
						}
						find^=(n-1);
						pw.print((n-1)+" ");
						for(int i=n;i<=1000000;i++) {
							int x1=find^i;
							if(x1>n-1 && x1!=i) {
								pw.println(i+" "+x1);
								break;
							}
						}
					}
				}
			}
		}
 	}
	private static void dfs(int cur,int prev,LinkedList<Integer>[] l,int[] arr,int c) {
		arr[cur]=c;
		Iterator<Integer> it=l[cur].listIterator();
		while(it.hasNext()) {
			int x=it.next();
			if(x!=prev) {
				dfs(x,cur,l,arr,(c+1)%2);
			}
		}
	}
	private static int[] buildSuffix(String s,int n){
		Integer[] order=new Integer[n];
		for(int i=0;i<n;i++) order[i]=n-i-1;
		Arrays.sort(order,(a,b) -> Character.compare(s.charAt(a),s.charAt(b)));
		int[] sa=new int[n];
		int[] m_tmp=new int[n];
		for(int i=0;i<n;i++){
			sa[i]=order[i];
			m_tmp[i]=s.charAt(i);
		}
		for(int len=1;len<n;len<<=1){
			int[] tmp=m_tmp.clone();
			m_tmp[sa[0]]=0;
			for(int i=1;i<n;i++){
				m_tmp[sa[i]] = (tmp[sa[i-1]]==tmp[sa[i]] && sa[i-1] + len < n && 
								tmp[(sa[i-1]+(len>>1))]==tmp[(sa[i]+(len>>1))]) ? m_tmp[sa[i-1]]:i;
			}
			int[] cnt=new int[n];
			for(int i=0;i<n;i++) cnt[i]=i;
			int[] sa_tmp=sa.clone();
			for(int i=0;i<n;i++){
				int s1=sa_tmp[i]-len;
				if(s1>=0)
					sa[cnt[m_tmp[s1]]++]=s1;
			}
		}
		return sa;
	}
	private static int[] buildLCP(int[] sa,String s,int n){
		int[] ind=new int[n];
		for(int i=0;i<n;i++)
			ind[sa[i]]=i;
		int[] lcp=new int[n];
		for(int i=0, k=0; i<n; i++)
			if(ind[i] < n-1){
				for(int j=sa[ind[i]+1]; Math.max(i,j)+k < n && s.charAt(i+k)==s.charAt(j+k);) k++;
				lcp[ind[i]]=k;
				if(k>0) k--;
			}
		return lcp;
	}
	private static class Edge{
		int u,v;
		public Edge(int a,int b) {
			u=a;v=b;
		}
	}
	private static void shortestPath(LinkedList<Edge>[] l,int n,int k,int[] masks) {
		int tot=(int) Math.pow(2,k);
		int[][] dist=new int[n][tot];
		int[][] from=new int[n][tot];
		for(int i=0;i<n;i++)
			Arrays.fill(dist[i], Integer.MAX_VALUE);
		dist[0][masks[0]]=0;
		from[0][masks[0]]=-1;
		PriorityQueue<Long> q=new PriorityQueue<>();
		q.add((long) masks[0]);
		//System.out.println(0);
		while(!q.isEmpty()) {
			long cur=q.poll();
			//System.out.println(cur);
			int u = ((int) cur)>>>10;
			int mask=(int) (cur&(tot-1));
			//System.out.println((u+1)+" "+mask+" "+dist[u][mask]);
			if((cur>>>32) != dist[u][mask])
				continue;
			//System.out.println((u+1)+" "+Integer.toBinaryString(mask)+" "+dist[u][mask]);
			Iterator<Edge> it=l[u].listIterator();
			while(it.hasNext()) {
				Edge e=it.next();
				int len=dist[u][mask]+e.v;
				if(dist[e.u][mask|masks[e.u]]>len) {
					//System.out.println((e.u+1)+" "+(mask|masks[e.u])+" "+len+" "+Long.toBinaryString(((long)len << 32)+(e.u<<10)+mask));
					dist[e.u][mask|masks[e.u]]=len;
					from[e.u][mask|masks[e.u]]=u;
					q.add(((long)len << 32)+(e.u<<10)+(mask|masks[e.u]));
				}
			}
		}
		int ans=Integer.MAX_VALUE;
		//System.out.println(Integer.toBinaryString(tot-1));
		for(int i=0;i<tot;i++) {
			for(int j=0;j<tot;j++) {
				//System.out.println(Integer.toBinaryString(i)+" "+Integer.toBinaryString(j)+" "+dist[n-1][i]+" "+dist[n-1][j]);
				if((i|j) != (tot-1))
					continue;
				//System.out.println(i+" "+j);
				ans=Math.min(ans,Math.max(dist[n-1][i],dist[n-1][j]));
			}
		}
		pw.println(ans);
	}
	private static class Pair1 implements Comparable<Pair1>{
		int dist, affected, u;
		public Pair1(int a) {
			dist=Integer.MAX_VALUE;
			affected=Integer.MAX_VALUE;
			u=a;
		}
		public int compareTo(Pair1 another) {
			return this.dist!=another.dist?this.dist-another.dist:this.affected-another.affected;
		}
	}
	static void multiply(long[][] a, long[][] b, long m)
	{
		int n = a.length;
		long[][] mul = new long[n][n];
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
			{
				mul[i][j] = 0;
				for (int k = 0; k < n; k++)
					mul[i][j] = (mul[i][j] + (a[i][k] * b[k][j]) % m) % m;
			}
		}
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				a[i][j] = mul[i][j];
	}
	private static class DSU{
		int[] parent;
		int[] rank;
		int[][] lr;
		public DSU(int n){
			parent=new int[n];
			rank=new int[n];
			lr=new int[n][2];
			//cnt=new int[n];
			for(int i=0;i<n;i++){
				parent[i]=i;
				rank[i]=1;
				lr[i][0]=lr[i][1]=i;
				//cnt[i]=1;
			}
		}
		int find(int i){
	        while(parent[i] !=i){
	        	parent[i]=parent[parent[i]];
	        	i=parent[i];
	        }
	        return i;
	    }
		int Union(int x, int y){
	        int xset = find(x);
	        int yset = find(y);
	        if(xset==yset)
	        	return 0;
	        	parent[yset]=xset;
	        	rank[xset]+=rank[yset];
	        	rank[yset]=0;
	        	lr[xset][1]=lr[yset][1];
	        	lr[yset][0]=lr[xset][0];
	        	//cnt[xset]+=cnt[yset];
	        	//cnt[yset]=0;
	        	return xset;
	    }
	}

	private static long pow(long a, long b, long c)
	{
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}
	private static int block;
	private static class Mo implements Comparable<Mo>
	{
		int l;
		int r;
		int i;

		public Mo(int a, int b, int ind)
		{
			l = a;
			r = b;
			i = ind;
		}

		@Override
		public int compareTo(Mo arg0)
		{
			int b1 = this.l / block;
			int b2 = arg0.l / block;
			return (b1 != b2) ? (b1 - b2) : (this.r - arg0.r);
		}
	}

	private static long gcd(long n, long l)
	{
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}
	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable()
		{
			@Override
			public void run()
			{
				InputReader(System.in);
				pw = new PrintWriter(System.out);
				soln();
				pw.close();
			}
		}, "1", 1 << 26).start();
	}

	public static void InputReader(InputStream stream1)
	{
		stream = stream1;
	}

	private static boolean isWhitespace(int c)
	{
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private static boolean isEndOfLine(int c)
	{
		return c == '\n' || c == '\r' || c == -1;
	}

	private static int read()
	{
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars)
		{
			curChar = 0;
			try
			{
				numChars = stream.read(buf);
			} catch (IOException e)
			{
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private static int nextInt()
	{
		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;
	}

	private static long nextLong()
	{
		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;
	}

	private static String nextToken()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static 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();
	}

	private static int[] nextIntArray(int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextInt();
		}
		return arr;
	}

	private static long[] nextLongArray(int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextLong();
		}
		return arr;
	}

	private static void pArray(int[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static void pArray(long[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static boolean isSpaceChar(int c)
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private static char nextChar()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}