KöMaL 2006 B3888

For what integers $m$>1 is there an ordering $a_1$,$a_2$,...,$a_m$ of the numbers 1,2,...,$m$, such that the sums $a_1$,$a_1$+$a_2$,...,$a_1$+$a_2$+...+$a_m$ leave different remainders when divided by $m$?