CMO 2011 Problem 4

Show that there exists a positive integer $N$ such that for all integers $a>N$, there exists a contiguous substring of the decimal expansion of $a$ that is divisible by 2011. (For instance, if $a=153204$, then 15, 532, and 0 are all contiguous substrings of $a$. Note that 0 is divisible by 2011 .)