Let $(a_n)$ and $(b_n)$ be the sequences of real numbers such that
\[ (2 + i)^n = a_n + b_ni \] for all integers $n\geq 0$, where $i = \sqrt{-1}$. Find the value of \[\sum_{n=0}^\infty\frac{a_nb_n}{7^n}\,.\] The original answer is in the form \(\frac{k}{m}\). Please give the value of \(k + m\).

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