Transformations · Superchallenge problem

The point $(0, 7)$ is reflected across the line $x = 1$, then across $x = 4$, then across $x = 1$, then across $x = 4$, and so on, alternating, for a total of $101$ reflections (the first and the last across $x = 1$). Find the $x$-coordinate of the final image.