The number $2013$ is expressed in the form    
$2013 = \frac {a_1!a_2!...a_m!}{b_1!b_2!...b_n!}$,    
where $a_1 \ge a_2 \ge \cdots \ge a_m$ and $b_1 \ge b_2 \ge \cdots \ge b_n$ are positive integers and $a_1 + b_1$ is as small as possible. Find the value of $|a_1 - b_1|$.

Let's think step by step and output the final answer within \boxed{}.
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