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.