You should aim for a solution as good or better than O(m * n) time and O(m * n) space, where m is the number of rows and n is the number of columns in the grid.

Try to think in terms of recursion and visualize it as a decision tree, where we have two choices at each step. Can you determine the base condition and recurrence relation?

We recursively traverse the grid using row i and column j. At each step, we explore both possibilities: moving down or moving right, ensuring we do not go out of bounds. If we reach the bottom-right cell, we return 1.

This approach has exponential complexity. Can you think of a way to optimize the recursion? Maybe you should consider using a dynamic programming approach.

We can use memoization to cache the results of recursive calls and avoid recalculations. A hash map or a 2D array can be used to store these results.