Laser Trajectory in a Fully Mirrored Room

Problem Statement

A square room sits on a flat floor. Define the floor as the $x$ - $y$ coordinate plane.

The four walls of the room stand along the following line segments, and all inner surfaces are ideal mirrors that reflect light perfectly.

South wall: $y = 0$ (for $0 \le x \le W$ )
North wall: $y = D$ (for $0 \le x \le W$ )
West wall: $x = 0$ (for $0 \le y \le D$ )
East wall: $x = W$ (for $0 \le y \le D$ )

A single, extremely narrow laser beam is fired into the room through a tiny gap at the southwest corner, the origin $(0, 0)$ .

The light travels in a straight line through the uniform space and reflects off walls following the law of reflection (angle of incidence equals angle of reflection) exactly.

The laser beam reflects first off the north wall, then off the east wall, and finally hits a tiny light-absorbing sensor embedded exactly at the midpoint of the south wall, $(W/2, 0)$ , where it is absorbed.

Find the total distance $L$ traveled by the laser beam from the origin $(0, 0)$ until it hits the sensor.

Constraints

$W = 36\,\text{m}$
$D = 36\,\text{m}$

Input Format

Find the total travel distance $L$ in $\text{m}$ and give the answer as a positive integer.

Problem Statement

Constraints

Input Format

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