KöMaL 2009 B4193

Out of a set of one million lottery tickets issued with numbers 000000 to 999999, a group of friends bought all tickets that they considered ``lucky'', that is the ones with numbers $\overline{abcdef}$ , such that $af$+$be$+$cd$=100. Prove that the sum of the numbers of the remaining tickets is divisible by 1001.