What is the value of the product 

\[\left(\frac{1\cdot3}{2\cdot2}\right)\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\cdots\left(\frac{97\cdot99}{98\cdot98}\right)\left(\frac{98\cdot100}{99\cdot99}\right)?\]

Provide your answer as a fraction in simplest 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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