XOR Folding

You are given a grid with size $N \times M$. Each cell of this grid contains either $0$ or $1$. We should perform the following operation until the size of the grid becomes $1 \times 1$: - Suppose the present size of the grid is $x \times y$. - Choose one of the $x-1$ horizontal lines or $y-1$ vertical lines crossing the grid. - Fold the grid along this line. For each pair of cells which overlap