The numbers $1$, $latex \frac{1}{2}$, $latex \frac{1}{3}$, $latex \ldots$, $latex \frac{1}{2018}$ are written on the blackboard. IU chooses any two numbers from blackboard, say $latex \alpha$ and $latex \beta$, erase them and instead writes the number $latex \alpha\beta + \alpha + \beta$. She continues to do this process until there is only one number left on the board. What are the possible values of the final number?

Due day is May 4.