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.math.BigInteger;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

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

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

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

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    int[] values;

    void shuffle(int[] values, Random random) {
        for (int i = 1; i < values.length; i++) {
            int prev = random.nextInt(i);
            int t = values[prev];
            values[prev] = values[i];
            values[i] = t;
        }
    }

    void solve() throws IOException {
        int n = readInt();
        int x = readInt();
        if (n == 2 && x == 0) {
            out.println("NO");
            return;
        }
        values = new int[1000000 + 1];
        for (int i = 0; i < values.length; i++) {
            values[i] = i;
        }
        int first = 1000000 - 200000;
        int[] answer = new int[n];
        int i = 0;
        for (; i < n - 12; i += 4) {
            for (int j = 0; j < 4; j++) {
                answer[i + j] = first + i + j;
            }
        }
        int[] end = calc(n - i, x);
        System.arraycopy(end, 0, answer, i, end.length);
        out.println("YES");
        for (int v : answer) out.print(v + " ");
    }

    int[] calc(int cnt, int targetXor) {
        Random random = new Random();
        while (true) {
            Set<Integer> set = new HashSet<>();
            int xor = 0;
            while (set.size() < cnt - 1) {
                set.add(random.nextInt(1000));
            }
            for (int x : set) {
                xor ^= x;
            }
            int addXor = xor ^ targetXor;
            if (set.contains(addXor)) continue;
            set.add(addXor);
            int[] res = new int[cnt];
            int i = 0;
            for (int x : set) {
                res[i++] = x;
            }
            return res;
        }
    }

}