Flora the frog starts at \(0\) on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance \(m\) with probability \(\frac{1}{2^m}\).

Find the probability that Flora will eventually land at \(10\). Express your answer as a fraction in simplest form \(\frac{k}{m}\), and then provide the value of \(k + m\).

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