Consider an array where each integer from $1$ to $N$ (inclusive) can be made by either adding or subtracting $2$ numbers in the array. More rigorously, for every integer $1\le n\le N$ there exists two indices $i,j$ $(i\ne j)$ such that $A_i+A_j=n$ or $A_i-A_j=n$. Furthermore, each array element must be an integer in the range $[1,N]$, though they do not have to be distinct.

Your goal is to find and construct such an array with a length of at most $M$.

Constraints

Points Awarded	$N$	$M$
6 points	$18\le N\le {10}^4$	$M=\lfloor 0.4N\rfloor$
9 points	$18\le N\le {10}^7$	$M=\lfloor \sqrt{2N}\rfloor$

Input Specification

The only line of input contains two integers $N$ and $M$.

Output Specification

The first line should contain an integer $L$, the length of the array $A$ you have found.

The next line should contain $L$ integers $A_i$ $(1\le A_i\le N)$, the elements of the array.

Sample Input

18 7

Sample Output

7
2 3 16 4 8 5 13