, 2018

Omar marks a sequence of 12 points on a straight line beginning with a point $O$, followed by a point $P$ with $OP=1$. He chooses the points so that each point is the midpoint of the two immediately following points. For example $O$ is the midpoint of $PQ$, where $Q$ is the third point he marks. What is the distance between the first point $O$ and the 12th point $Z$?

(A) $171$ (B) $341$ (C) $512$ (D) $587$ (E) $683$