MathNet 2012 Question 75

An elf chooses two odd numbers $x,y$ with $0\lt y\lt x\lt 2012$, calculates $x^2-y^2$, and writes the result on paper. Every morning, starting the following day, he reads the number; if it is even, he replaces it by half its value and plays a prank on someone. The first morning he reads an odd number, he disappears back into the fairy world. What is the greatest number of pranks he can play?
(A) 11 (B) 12 (C) 14 (D) 21 (E) 22.