So, I was looking through my notes to find what I've written in my spare time. Turns out, I have this problem written in one of the notes.

I have an $$$N \times N$$$ square grid that needs to be fully covered with tiles. I can only use square tiles with the size of $$$i \times i$$$ where $$$1 \leq i \leq M$$$ to fill it. What is the minimum number of tiles needed to be used to fully cover the grid?

For example: If $$$N = 9$$$ and $$$M = 5$$$, then the minimum number of tiles needed is $$$9$$$, since I can use nine $$$3 \times 3$$$ square tiles to fully cover the $$$9 \times 9$$$ grid.

Constraint: $$$1 \leq M \leq N$$$

Further Constraint: idk, since I don't know the fastest complexity for this.

What is the fastest complexity and how to achieve it? Is it just brute force or is there an efficient algorithm to solve this?