Consider the Harmonic Table:
\[
\begin{array}{c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c@{\hspace{15pt}}c}
&&&1&&&\\
&&\tfrac{1}{2}&&\tfrac{1}{2}&&\\
&\tfrac{1}{3}&&\tfrac{1}{6}&&\tfrac{1}{3}&\\
\tfrac{1}{4}&&\tfrac{1}{12}&&\tfrac{1}{12}&&\tfrac{1}{4}\\
&&&\vdots&&&
\end{array}
\]
where $a_{n,1}=\frac{1}{n}$ and $a_{n,k+1}=a_{n-1,k}-a_{n,k}$. Find the remainder when the sum of the reciprocals of the $2007$ terms on the $2007^\text{th}$ row gets divided by $2008$.

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