Junior Mathematical Olympiad 2006 Q16

[JMO 2006 B5 Edited] An intelligent bug starts at the point (4,0) and follows these instructions: (i) First face “East” and walk one unit to the point (5,0); (ii) From then one, whenever you arrive at a point $\left(x,y\right)$ with $x$ and $y$ both integers, either turn left through 90 if $x-y$ is a multiple of 4 or is 1 more than a multiple of 4; or turn right through 90 if $x-y$ is 2 more than a multiple of 4 or is 3 more than a multiple of 4; and then walk one unit to the next point whose coordinates are both integers. After one move, the bug is at the point (5,0). At what coordinate will the bug be after 50 moves?