Suppose that $m$ and $n$ are relatively prime positive integers with $A = \frac{m}{n}$, where
\[ A = \frac{2+4+6+\dots+2014}{1+3+5+\dots+2013} - \frac{1+3+5+\dots+2013}{2+4+6+\dots+2014}. \] 
Find $m$. In other words, find the numerator of $A$ when $A$ is written as a fraction in simplest form.

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