Lily has an unfair coin that has a \(\frac{2}{3}\) probability of showing heads and a \(\frac{1}{3}\) probability of showing tails. She flips the coin twice. What is the probability that the first flip is heads while the second is tails? Provide your answer in the form of \(\frac{k}{m}\), where the fraction is in simplest form, and find the value of k + m.

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