Problem: We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.

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A pyramid with N=4 steps

Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:

* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.



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Writing integers into the blocks

Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.

Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.

Constraints

* 2≤N≤10^5
* 1≤x≤2N-1

Input

The input is given from Standard Input in the following format:


N x


Output

If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.

Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.

The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.

Examples

Input

4 4


Output

Yes
1
6
3
7
4
5
2


Input

2 1


Output

No

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.stream.IntStream;
import java.io.UncheckedIOException;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BMedianPyramidEasy solver = new BMedianPyramidEasy();
        solver.solve(1, in, out);
        out.close();
    }

    static class BMedianPyramidEasy {
        private static final String YES = "Yes";
        private static final String NO = "No";

        public void solve(int testNumber, LightScanner in, PrintWriter out) {
            int n = in.ints(), x = in.ints();
            if (x == 1 || x == 2 * n - 1) {
                out.println(NO);
                return;
            }
            out.println(YES);
            int[] ans = new int[2 * n - 1];
            if (x == 2 * n - 2 && n > 2) {
                ans[n - 2] = x - 2;
                ans[n - 1] = x + 1;
                ans[n] = x;
                ans[n + 1] = x - 1;
                int m = 1;
                for (int i = 0; i < 2 * n - 1; i++) {
                    if (i == n - 2) {
                        i = n + 2;
                        if (i >= 2 * n - 1) {
                            break;
                        }
                    }
                    if (m == x - 2) {
                        m = x + 2;
                    }
                    ans[i] = m;
                    m++;
                }
            } else {
                ans[n - 2] = x + 1;
                ans[n - 1] = x;
                ans[n] = x - 1;
                if (n > 2) {
                    ans[n + 1] = x + 2;
                }
                int m = 1;
                for (int i = 0; i < 2 * n - 1; i++) {
                    if (i == n - 2) {
                        i = n + 2;
                        if (i >= 2 * n - 1) {
                            break;
                        }
                    }
                    if (m == x - 1) {
                        m = x + 3;
                    }
                    ans[i] = m;
                    m++;
                }
            }
            Arrays.stream(ans).forEach(out::println);
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

    }
}