2015 AMC 10B Problem 24

Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin p_0=(0,0) facing to the east and walks one unit, arriving at p_1=(1,0). For n=1,2,3,\ldots, right after arriving at the point p_n, if Aaron can turn 90^\circ left and walk one unit to an unvisited point p_{n+1}, he does that. Otherwise, he walks one unit straight ahead to reach p_{n+1}. Thus the sequence of points continues p_2=(1,1), p_3=(0,1), p_4=(-1,1), p_5=(-1,0), and so on in a counterclockwise spiral pattern. What is p_{2015}?

\textbf{(A) } (-22,-13)\qquad\textbf{(B) } (-13,-22)\qquad\textbf{(C) } (-13,22)\qquad\textbf{(D) } (13,-22)\qquad\textbf{(E) } (22,-13)

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.