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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		new Main().solve();
	}
	void solve(){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		n=2*n-1;
		int x=sc.nextInt();
		if(n==1){
			if(x==1){
				System.out.println("Yes");
				System.out.println(1);
				return;
			}else{
				System.out.println("No");
				return;
			}
		}
		if(n==3){
			if(x==2){
				System.out.println("Yes");
				System.out.println(1);
				System.out.println(2);
				System.out.println(3);
				return;
			}else{
				System.out.println("No");
				return;
			}
		}
		if(x==1 || x==n){
			System.out.println("No");
			return;
		}else{
			System.out.println("Yes");
			int count=0;
			for(int i=1;i<=n;i++){
				if(count==(n-5)/2){
					if(x-2==0){
						System.out.println(x+2);
						System.out.println(x-1);
						System.out.println(x);
						System.out.println(x+1);
						System.out.println(x+3);
					}else if(x+2==n+1){
						System.out.println(x-3);
						System.out.println(x-1);
						System.out.println(x);
						System.out.println(x+1);
						System.out.println(x-2);
					}else{
						System.out.println(x+2);
						System.out.println(x-1);
						System.out.println(x);
						System.out.println(x+1);
						System.out.println(x-2);
					}
					count+=5;
				}
				if(x-2==0 && i==x+3)continue;
				if(x+2==n+1 && i==x-3)continue;
				if(i>=x-2 && i<=x+2)continue;
				else{
					System.out.println(i);
					count++;
				}
			}
		}
	}
	
}