PAMO 2012 Problem 4

The numbers $\frac{1}{1}, \frac{1}{2}, \cdots , \frac{1}{2012}$ are written on the blackboard. Aïcha chooses any two numbers from the blackboard, say $x$ and $y$ , erases them and she writes instead the number $x + y + xy$ . She continues to do this until only one number is left on the board. What are the possible values of the final number?