The Minnesota Twins face the New York Mets in the 2006 World Series. Assuming the two teams are evenly matched (each has a \(0.5\) probability of winning any game), find the probability that the World Series (a best of 7 series of games which lasts until one team wins four games) will require the full seven games to determine a winner. The original answer is in \(\frac{k}{m}\) format, please give the value of k + m.

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