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.



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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.PrintWriter;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n= sc.nextInt();
		int x = sc.nextInt();
		sc.close();

		if(x == 1 || x == n*2-1){
			System.out.println("No");
		}else{
			System.out.println("Yes");
			if(x>n){
				for(int i=n; i<n*2; i++){
					if(i!=x){
						//System.out.println(i);
						out.println(i);
					}
					if(i%100 == 0){
						out.flush();
					}
				}
				out.flush();
				//System.out.println(x);
				out.println(x);
				for(int i=1; i<n; i++){
					if(i!=x){
						//System.out.println(i);
						out.println(i);
					}
					if(i%100 == 0){
						out.flush();
					}
				}
			}else{
				for(int i=n+1; i<n*2; i++){
					if(i!=x){
						//System.out.println(i);
						out.println(i);
					}
					if(i%100 == 0){
						out.flush();
					}
				}
				out.flush();
				//System.out.println(x);
				out.println(x);
				for(int i=1; i<n+1; i++){
					if(i!=x){
						//System.out.println(i);
						out.println(i);
					}
					if(i%100 == 0){
						out.flush();
					}
				}
			}
		}
		out.flush();
	}

}