Ada Bishop

Ada has the biggest chessboard in ChefLand. It has $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$), where $M \ge 2N$. As training for her upcoming world chess championship match, she placed one bishop at row $r$ and column $c$ of her board. The remaining squares of the board are empty. Now, she is calculating the number of squares that can be reached by the bishop in