IMO 2009 Problem 6

Let $a_1, a_2, \ldots , a_n$ be distinct positive integers and let $M$ be a set of $n - 1$ positive integers not containing $s = a_1 + a_2 + \ldots + a_n.$ A grasshopper is to jump along the real axis, starting at the point $0$ and making $n$ jumps to the right with lengths $a_1, a_2, \ldots , a_n$ in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in $M.$

Proposed by Dmitry Khramtsov, Russia