Avoid Alternating

You have a grid with $N$ rows and $M$ columns in which $K$ cells are black and the rest are white. Let $(i, j)$ represent the cell in the $i$-th row from the top and the $j$-th column from the left. If you are currently at cell $(i, j)$, you can: - move one cell down to $(i + 1, j)$ - move one cell right to $(i, j + 1)$ The cost of a path is defined as the number of times you move between two