KöMaL 2013 B4505

We have two containers with volumes of $p$ litres and of $q$ litres. It is allowed to fill up completely or empty either container at a tap, to fill up either container completely from the other one, and to pour the entire content of one into the other. Prove that if $p$>$q$ are relatively prime positive integers, and $s$is a positive integer such that $s \le p$, then it is possible to achieve that one container have exactly $s$ litres of water in it.