OMM 2019 Problem 5

Let $a > b$ be relatively prime positive integers. A grashopper stands at point $0$ in a number line. Each minute, the grashopper jumps according to the following rules:

• If the current minute is a multiple of $a$ and not a multiple of $b$ , it jumps $a$ units forward.
• If the current minute is a multiple of $b$ and not a multiple of $a$ , it jumps $b$ units backward.
• If the current minute is both a multiple of $b$ and a multiple of $a$ , it jumps $a - b$ units forward.
• If the current minute is neither a multiple of $a$ nor a multiple of $b$ , it doesn't move.

Find all positions on the number line that the grasshopper will eventually reach.