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.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
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskB {
		int[] ans;
		boolean[] used;
		int p;

		public void solve(int testNumber, FastScanner in, PrintWriter out) {
			int n = in.nextInt();
			int x = in.nextInt();
			if (x == 1 || x == 2 * n - 1) {
				out.println("No");
				return;
			}
			if (n == 2) {
				if (x == 2) {
					out.println("Yes");
					out.println("1");
					out.println("2");
					out.println("3");
				} else {
					out.println("No");
				}
				return;
			}
			ans = new int[2 * n - 1];
			used = new boolean[2 * n];
			p = 1;
			put(n - 2, 2 * n - 1);
			put(n - 1, x);
			put(n, 1);
			for (int i = 2 * n - 1; i > 0; i--) {
				if (!used[i]) {
					put(n + 1, i);
					break;
				}
			}
			for (int i = 0; i < ans.length; i++) {
				if (ans[i] == 0) {
					putAnything(i);
				}
			}
			out.println("Yes");
			for (int u : ans) {
				out.println(u);
			}
			// show(ans);
		}

		private void put(int pos, int x) {
			ans[pos] = x;
			used[x] = true;
		}

		private void putAnything(int pos) {
			while (p < used.length && used[p]) {
				++p;
			}
			put(pos, p);
		}

	}

	static class FastScanner {
		private BufferedReader in;
		private StringTokenizer st;

		public FastScanner(InputStream stream) {
			in = new BufferedReader(new InputStreamReader(stream));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(in.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}

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

	}
}