A list of \(8\) numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Given that the last three numbers are \(16\), \(64\), and \(1024\), find the first number in the list. The original answer is in \(\frac{k}{m}\) format, where \(\frac{k}{m}\) is a simplified fraction. Please provide the value of \(k + m\).

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