Sussy Rooks

You have an $N \times M$ grid. The grid can be filled with the values $0$ and $1$ only. Initially, **all** the cells of the grid are filled with value $0$. You start from the cell $(1,1)$. When you are at position $(i,j)$, you can do one of the following: - Change $A_{(i,j)}$ to $1$ and go to cell $(i+1,j+1)$. - Keep $A_{(i,j)}$ as $0$ and go to cell $(i+1,j)$ or $(i,j+1)$. If, at some point