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 {
    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    static final int[][] STEPS = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};

    void solve() throws IOException {
        int n = readInt(), x = readInt();
        if(n==2&&x==0){
            out.println("NO");
            return;
        }
        int flag = 0;
        TreeSet<Integer> answer = new TreeSet<Integer>();
        n--;
        while (n-- > 0) {
            flag = (int) (Math.random() * (200 * 1000));
            while (answer.contains(flag)) flag = (int) (Math.random() * (2000 * 100));
            if (n == 0) {
                while (answer.contains(x ^ flag) || answer.contains(flag)) {
                    flag = (int) (Math.random() * 200000);
                }
            }
            answer.add(flag);
            x ^= flag;
            if (flag > 1000 * 1000) {
                out.println("NO");
                return;
            }
        }

        answer.add(x);
        out.println("YES");
        for (int i : answer) {
            out.print(i + " ");
        }
    }


    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
        tok = new
                StringTokenizer("");
    }

    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) {
            min = Math.min(min, value);
        }
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) {
            max = Math.max(max, value);
        }
        return max;
    }

    long minLong(long... values) {
        long min = Long.MAX_VALUE;
        for (long value : values) {
            min = Math.min(min, value);
        }
        return min;
    }

    long maxLong(long... values) {
        long max = Long.MIN_VALUE;
        for (long value : values) {
            max = Math.max(max, value);
        }
        return max;
    }

    boolean checkIndex(int index, int size) {
        return (0 <= index && index < size);
    }

    int abs(int a) {
        return Math.abs(a);
    }

    int gcd(int a, int b) {
        if (a * b == 0) return maxInt(a, b);
        else return gcd(minInt(a, b), maxInt(a, b) % minInt(a, b));
    }

    public static void main(String[] args) {
        new Main().run();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;


    void run() {
        try {
            long timeStart = System.currentTimeMillis();

            init();
            solve();

            out.close();

            long timeEnd = System.currentTimeMillis();
            System.err.println("time = " + (timeEnd - timeStart) + " compiled");
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }


    }

    String readLine() throws IOException {
        return in.readLine();
    }

    String delimiter = " ";

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine)
                return null;

            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken(delimiter);
    }

    int[] readIntArray(int b) {
        int a[] = new int[b];
        for (int i = 0; i < b; i++) {
            try {
                a[i] = readInt();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return a;
    }

    long[] readLongArray(int b) {
        long a[] = new long[b];
        for (int i = 0; i < b; i++) {
            try {
                a[i] = readLong();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return a;
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }


    void sortArrayInt(int[] a) {
        Integer arr[] = new Integer[a.length];
        for (int i = 0; i < a.length; i++) {
            arr[i] = a[i];
        }
        Arrays.sort(arr);
        for (int i = 0; i < a.length; i++) {
            a[i] = arr[i];
        }
    }

    void sortArrayLong(long[] a) {
        Long arr[] = new Long[a.length];
        for (int i = 0; i < a.length; i++) {
            arr[i] = a[i];
        }
        Arrays.sort(arr);
        for (int i = 0; i < a.length; i++) {
            a[i] = arr[i];
        }
    }


}