Question 20
The number $2013$ is expressed in the form $$
2013 = \frac {a_1!a_2!\cdots a_m!}{b_1!b_2!\cdots b_n!},
$$ 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. What is $|a_1 - b_1|?$
2013 = \frac {a_1!a_2!\cdots a_m!}{b_1!b_2!\cdots 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. What is $|a_1 - b_1|?$