Chococut

Alice has a rectangular bar of chocolate of dimensions $N\times M$. The bar is made up of $N\cdot M$ smaller $1\times 1$ squares. Unfortunately, Alice has to share part of the chocolate with Bob. **At most once**, Alice can break the rectangular bar into two smaller rectangles, either by making a vertical cut or a horizontal cut. She'll then give one of the pieces to Bob, and keep the other for