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.lang.reflect.Array;
import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int x = Integer.parseInt(st.nextToken());
        if(x == 1 || x == 2*n - 1){
            System.out.print("No");
            return;
        }
        System.out.println("Yes");
        StringBuilder sb = new StringBuilder();
        int array[] = new int[2*n];
        array[n] = x;
        for(int i = n - 1;i >= 1;i--)
            array[i] = array[i + 1] - 1;
        for(int i = n + 1;i < array.length;i++)
            array[i] = array[i - 1] + 1;
        for(int i = 1;i < array.length;i++){
            if(array[i] <= 0)array[i] += 2*n - 1;
            if(array[i] > 2*n - 1)array[i] -= 2*n - 1;
        }
        for(int i = 1;i < 2*n;i++){
            sb.append(array[i]);
            sb.append('\n');
        }
        System.out.print(sb);
    }
}