Ceiling Sum

You are given two integers $A, B$. You have to choose an integer $X$ in the range [minimum($A, B$), maximum($A, B$)] such that: $$\Big \lceil \frac{B - X}{2} \Big \rceil + \Big \lceil \frac{X - A}{2} \Big \rceil$$ is maximum. What is the maximum sum you can obtain if you choose $X$ optimally? **Note:** $\lceil x \rceil$ : Returns the smallest integer that is greater than or equal to $x$ (i.e