Point Grid

Suppose we have a 2D grid $A$ of infinite width and height of $N$ units. Each row of the grid can be represented in the form of $111\ldots100\ldots \infty$ where the $1$s are repeated $x$ times, $x > 0$. Implying that the row starts with $x$ consecutive $1$-s followed by all $0$-s. Initially all cells are unmarked. Cell (i,j) refers to the i-th row, and j-th column. (1,1) refers to the bottom-le