# That Creepy Extra Area Under the Stairs

Start in the lower left corner of a 5x10 unit grid. You may only move to the right and upward along the edges to get to the top right corner. The area of a path between the corners is the amount of area beneath the line in square units. For example:

On a 5x10 grid, how many different paths from the lower left corner to the upper right corner have an area congruent to 1 mod 5?

Bonus: Choose any prime $$p$$ and positive integers $$i<p$$, $$j$$ and $$k$$ and generalize this solution to the number of paths with an area congruent to $$i$$ mod $$p$$ on a $$jp$$ by $$kp$$ grid.

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