KöMaL 2009 A496

Let $a_1$,$a_2$,...,$a_{2k}$ be distinct integers and let $M$ be a set of $k$ integers not containing 0 and $s$=$a_1$+$a_2$+...+$a_{2k}$. A grasshopper is to jump along the real axis, starting at the point 0 and making 2$k$ jumps with lengths $a_1$,$a_2$,...,$a_{2k}$ in some order. If $a_i$>0 then the grasshopper jumps to the right; while if $a_i$<0 then the grasshopper jumps to the left, to the point in the distance |$a_i$| in the respective steps. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in $M$.