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