If \(q_1(x)\) and \(r_1\) are the quotient and remainder, respectively, when the polynomial \(x^8\) is divided by \(x + \frac{1}{2}\), and if \(q_2(x)\) and \(r_2\) are the quotient and remainder, respectively, when \(q_1(x)\) is divided by \(x + \frac{1}{2}\), find the value of \(r_2\). The original answer is in the form \(-\frac{k}{m}\). Please provide the value of \(k + m\).

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