Treasure Hunt

You are given a grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). Let's denote the cell in row $r$ and column $c$ by $(r, c)$. Two cells of the grid are *adjacent* if they share a side. Some of the cells of this grid contain treasures. You do not know exactly which cells contain them, but an analysis of the grid, called a treasure hunt map, is available.