An ice ballerina rotates at a constant angular velocity at one particular point, meaning she does not translationally move. Her arms are fully extended as she rotates, and her moment of inertia is \(I\). Now, she pulls her arms in, and her moment of inertia becomes \(\frac{7}{10}I\). What is the ratio of the new kinetic energy (arms in) to the initial kinetic energy (arms out)? The original answer is in the format \(\frac{k}{m}\), please give the value of \(k + m\).

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