A man with mass $m$ jumps off a high bridge with a bungee cord attached to his ankles. The man falls through a maximum distance $H$ at which point the bungee cord brings him to a momentary rest before he bounces back up. The bungee cord is perfectly elastic, obeying Hooke's force law with a spring constant $k$, and stretches from an original length of $L_0$ to a final length $L = L_0 + h$. The maximum tension in the bungee cord is four times the weight of the man.

Find the maximum extension of the bungee cord $h$ in terms of $H$. 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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