Secret of Chocolate Poles

Wendy runs a chocolate shop and wants to display poles of chocolate disks in her showcase. She has three kinds of disks: white thin disks, dark thin disks, and dark thick disks. A thin disk is $1$ cm thick and a thick disk is $k$ cm thick. The disks are piled inside glass cylinders.

Every pole must satisfy all of the following conditions.

• A pole contains at least one disk.
• The total thickness of the disks in a pole is at most $l$ cm.
• The top disk and the bottom disk of a pole are dark.
• A disk placed directly on a white disk is dark, and a disk placed directly on a dark disk is white.

Figure A.1 shows six side views of poles. When $l = 5$ and $k = 3$, these six are the only side views Wendy can make.

Figure A.1. Six chocolate poles for $l = 5$ and $k = 3$

Given $l$ and $k$, count the distinct side views Wendy can make.

The input is a single test case in the following format.

l k

$l$ is the largest total thickness a pole may have, in centimeters, and $k$ is the thickness of a thick disk, in centimeters. $l$ and $k$ are integers with $1 \le l \le 100$ and $2 \le k \le 10$.

Print the number of distinct patterns.