Given an envelope, at most ~N~ stamps are allowed to be pasted. Calculate how to design the face value of stamps so for the maximum value ~MAX~ where every postage between ~1~ and ~MAX~ can be obtained if given ~K~ (~N+K \le 13~) types of stamps (assuming there are infinitely many stamps of each type).

For example, ~N = 3~, ~K = 2~, if the face values are ~1~ cent and ~4~ cents, then every postage between ~1 \sim 6~ cents will be able to be obtained. Every postage between ~1 \sim 7~ cents can be obtained if the face values are ~1~ cent, and ~3~ cents, respectively. It can be proven that when ~N = 3~, ~K = 2~, ~7~ cents is the maximum continuous postage that can be obtained, so ~MAX = 7~ and the face values are ~1~ cent and ~3~ cents respectively.

Input Specification

The input contains two integers, ~N~ and ~K~.

Output Specification

There should be two lines of output.

The first line of output should contain the face values chosen to maximize ~MAX~ in increasing order.

Output MAX=S on the second line, where ~S~ represents the maximum postage that can be obtained.

Sample Input

3 2

Sample Output

1 3
MAX=7

Problem translated to English by Tommy_Shan.