Gritty Grid

Alice and Bob are trapped in a grid having $N$ rows and $M$ columns. Alice is currently at cell $(1, 1)$ and Bob is at cell $(N, M)$ and they both want to meet each other at any common cell. But they have some restrictions in the way they can move and meet: A _step_ is defined as moving to an adjacent cell from the current cell that the person is in. So in a single step, if a person is at $(X, Y)