Water Transfer

The city of Hunterland can be represented as a grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). Let's denote a cell in row $r$ and column $c$ by $(r,c)$. Ahmet, the mayor, plans to develop the underground water system of Hunterland. There is a large reservoir of water in the cell $(1, 1)$. Water from the reservoir must reach the cell $(N, M)$ through a s