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.ArrayList;
import java.util.StringTokenizer;

public class Solution {

    public static void solve(InputReader in, PrintWriter out, DebugWriter debug) throws IOException {
        int n = in.nextInt();
        int x = in.nextInt();
/*
        Random rand = new Random();
        int count = 0;
        while (true) {
            count++;
            if (count % 100 == 0) System.out.println(count);

            n = rand.nextInt(100000)+1;
            x = rand.nextInt(100001);
*/
            if (n == 1) {
                out.println("YES");
                out.print(x);
                return;
            }

            if (n == 2 && x != 0) {
                out.println("YES");
                out.print(x + " " + "0");
                return;
            }

            if (n == 2 && x == 0) {
                out.println("NO");
                return;
            }

            ArrayList<Integer> ans = new ArrayList<>();
            for (int i = 0; i < n - 2; i++) {
                ans.add(i + 1);
            }

            int needNumber, allXOR;
            int startRemove = 1;
            do {

                allXOR = 0;
                for (int i = 0; i < ans.size(); i++) {
                    allXOR ^= ans.get(i);
                }

                needNumber = x ^ allXOR;

                if (needNumber == 0){
                    ans.remove((Integer) startRemove);
                    ans.add(n+startRemove);
                    startRemove++;
                }

            } while (needNumber == 0);


                if (ans.contains(needNumber)) {
                    ans.remove((Integer) needNumber);

                    int len = Integer.toBinaryString(n - 2).length();
                    String bin1 = "11", bin2 = "10", bin3 = "01";
                    for (int i = 0; i < len; i++) {
                        bin1 += "1";
                        bin2 += "1";
                        bin3 += "0";
                    }
                    ans.add(Integer.parseInt(bin1, 2));
                    ans.add(Integer.parseInt(bin2, 2));
                    ans.add(Integer.parseInt(bin3, 2));
                } else {
                    ans.add(needNumber);
                    ans.add(0);
                }

            int result = 0;
            for (int i = 0; i < ans.size(); i++) {
                result ^= ans.get(i);
            }
/*
            if (result != x){
                debug.println("WRONG: " + result + " != " + x + " (" + n + ")");
                System.out.println(n + " " + x);
                return;
            }

            TreeSet<Integer> set = new TreeSet<>();
            for (int i : ans) set.add(i);
            if (ans.size() != set.size()){
                debug.println("DUPLICATE: " + set.size() + " != " + n);
                System.out.println(n + " " + x);
                return;
            }
            if (ans.size() != n){
                debug.println("WRONG SIZE: " + ans.size() + " != " + n);
                System.out.println(n + " " + x);
                return;
            }
*/

            debug.println("x: " + Integer.toBinaryString(x));
            debug.println("all xor: " + Integer.toBinaryString(allXOR));
            debug.println("need: " + Integer.toBinaryString(needNumber));
            debug.println("result: " + Integer.toBinaryString(result) + " (" + result + ")");


            out.println("YES");
            for (int i = 0; i < ans.size(); i++) {
                out.print(ans.get(i) + " ");
            }

        //}
    }

    public static void main(String[] args) throws IOException{
        InputReader in;
        PrintWriter out;
        DebugWriter debug;

        if (args.length > 0 && args[0].equals("file")) {
            in = new InputReader(new BufferedReader(new FileReader("input.txt")));
            out = new PrintWriter(new FileWriter("output.txt"));
            debug = new DebugWriter(true);

            int sampleNumber = 1;
            do {
                String nextSample = "Sample #" + sampleNumber++ + ": ";
                out.println(nextSample);
                debug.println(nextSample);

                solve(in, out, debug);

                out.println("");
                debug.println("");
            } while (in.reader.readLine() != null);
        } else {
            in = new InputReader(new BufferedReader(new InputStreamReader(System.in)));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            debug = new DebugWriter(false);

            solve(in, out, debug);
        }

        in.reader.close();
        out.close();
    }

    public static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(BufferedReader reader) {
            this.reader = reader;
            tokenizer = null;
        }

        public String next() throws IOException{
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }

            return tokenizer.nextToken();
        }

        public int nextInt() throws IOException{
            return Integer.parseInt(next());
        }

        public int[] nextIntArray(int n) throws IOException{
            int[] array = new int[n];
            for (int i=0; i<n; i++){
                array[i] = nextInt();
            }

            return array;
        }
    }

    public static class DebugWriter {
        public boolean enable;

        public DebugWriter(boolean enable){
            this.enable = enable;
        }

        public void print(Object o){
            if (enable) System.out.print(o);
        }

        public void println(Object o){
            if (enable) System.out.println(o);
        }
    }

}