Kata

You are an undergrad at Carnegie Mellon University, and you like coffee a lot.

However, navigating to the coffee machine is no trivial task. After getting lost in the building several times, you decide to draw a map of the current floor to aid your coffee retrieval.

An example map looks like this:

+ - - + - - + - - +
|     |     |     |
+ - - + - - + - - +
|     |     |     |
+ - - + - - + - - +

Each line represents a corridor (or pathway), and + represents an intersection.

You are currently at the top-left intersection, while the coffee machine is located at the most bottom-right intersection. Assuming that you can only go down or right, figure out how many possible routes there are to the coffee machine.

Input

width and height

width and height each specifies the amount of corridor intersections on that axis. In the example provided above, width = 4 and height = 3.

As another example, a map of width = 3 and height = 2 looks like:

+ - - + - - +
|     |     |
+ - - + - - +

Output

Your function should return the total possible routes from your position (top-left) to the coffee machine (bottom-right) while only going down or right.

Consider this minimal example of width = 2 and height = 2:

+ - - +
|     |
+ - - +

You can either go ['right', 'down'] or ['down', 'right'], therefore there are 2 possible routes.

Good luck!