Binary Board

Chef loves single-colored squares, so he got a rectangular board with size $N \times M$ consisting only of black cells and white cells. He calculates the *cost* of the board in the following manner: - Let's denote the number of ways to choose $k^2$ white cells which form a square with edge length $k$ (and edges parallel to the borders of the board) by $W_k$. For example, a $2 \times 3$ board consi