A red ball and a green ball are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability that it is tossed into bin \(k\) is \(2^{-k}\) for \(k = 1,2,3,\ldots\). What is the probability that the red ball is tossed into a higher-numbered bin than the green ball? 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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