Minimum Coloring

There is a matrix of size $N \times M$. Two **distinct** cells of the matrix $(x_1, y_1)$ and $(x_2, y_2)$ are painted with colors $\text{1}$ and $\text{2}$ respectively. You have to paint the **remaining** cells of the matrix such that: - No two adjacent cells are painted in same color. - Each color is an integer from $1$ to $10^9$ (both inclusive). - The number of **distinct** colors used is *