What is the value of \(\frac{1}{3}\cdot\frac{2}{4}\cdot\frac{3}{5}\cdots\frac{18}{20}\cdot\frac{19}{21}\cdot\frac{20}{22}?\) The answer is in the form \(\frac{k}{m}\). Please calculate the value of \(k + m\).

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