Notice that the problem is asking you to find the solution to the following problem:

f(N) = f(N-a) + f(N-b), where f(0) = 1

Since N can be quite large, you cannot simply solve bottom up, as this would be O(N). The correct approach is to utilize matrix exponentiation to solve recurrence relations. I recommend a google search for doing this with a simple recurrence relation to start, fibonacci. After that, you will see that this is easily solved in a similar way.