2013 AMC 12B Problem 15

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 ... \ge a_m and b_1 \ge b_2 \ge ... \ge b_n are positive integers and a_1 + b_1 is as small as possible. What is |a_1 - b_1|?

\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.