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.

<image>

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.



<image>

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.*;
import java.util.*;


public class Main {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int n = sc.nextInt();
		int x = sc.nextInt();

		if (n == 2 && x != 2) {
			pr.println("No");
			return;
		} else if (n == 2 && x == 2) {
			pr.println("Yes");
			int[] ans = {1, 2, 3};
			for (int e : ans) {
				pr.println(e);
			}
			return;
		}

		if (n == 3 && x == 2) {
			pr.println("Yes");
			int[] ans = {5, 2, 1, 4, 3};
			for (int e : ans) {
				pr.println(e);
			}
			return;
		} else if (n == 3 && x == 4) {
			pr.println("Yes");
			int[] ans = {1, 2, 5, 4, 3};
			for (int e : ans) {
				pr.println(e);
			}
			return;
		} else if (n == 3 && x == 3) {
			pr.println("Yes");
			int[] ans = {1, 2, 3, 4, 5};
			for (int e : ans) {
				pr.println(e);
			}
			return;
		} else if (n == 3) {
			pr.println("No");
			return;
		}

		if (x <= 1 || x >= 2 * n - 1) {
			pr.println("No");
		} else if (x == 2) {
			pr.println("Yes");
			int[] ans = new int[2 * n - 1];
			ans[n - 1] = x - 1;
			ans[n - 2] = x;
			ans[n] = x + 1;
			ans[n - 3] = x + 2;
//			ans[n + 1] = x - 1;
			int j = 0;
			for (int i = 1; i < x - 1; i++) {
				if (j == n - 3) {
					j = n + 1;
				}
				ans[j++] = i;
			}
			for (int i = x + 3; i <= 2 * n - 1; i++) {
				if (j == n - 3) {
					j = n + 1;
				}
				ans[j++] = i;
			}

			for (int i = 0; i < 2 * n - 1; i++) {
				pr.println(ans[i]);
			}
		} else if (x == 2 * n - 2) {
			pr.println("Yes");
			int[] ans = new int[2 * n - 1];
			ans[n - 1] = x + 1;
			ans[n - 2] = x;
			ans[n] = x - 1;
			ans[n - 3] = x - 2;
//			ans[n + 1] = x - 1;
			int j = 0;
			for (int i = 1; i < x - 2; i++) {
				if (j == n - 3) {
					j = n + 1;
				}
				ans[j++] = i;
			}
			for (int i = x + 2; i <= 2 * n - 1; i++) {
				if (j == n - 3) {
					j = n + 1;
				}
				ans[j++] = i;
			}

			for (int i = 0; i < 2 * n - 1; i++) {
				pr.println(ans[i]);
			}
		} else {
			pr.println("Yes");
			int[] ans = new int[2 * n - 1];
			ans[n - 1] = x;
			ans[n - 2] = x - 2;
			ans[n] = x + 1;
			ans[n - 3] = x + 2;
			ans[n + 1] = x - 1;
			int j = 0;
			for (int i = 1; i < x - 2; i++) {
				if (j == n - 3) {
					j = n + 2;
				}
				ans[j++] = i;
			}
			for (int i = x + 3; i <= 2 * n - 1; i++) {
				if (j == n - 3) {
					j = n + 2;
				}
				ans[j++] = i;
			}

			for (int i = 0; i < 2 * n - 1; i++) {
				pr.println(ans[i]);
			}
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);

		solve();

		pr.close();
		sc.close();
	}

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}