Can You Read My Mind?

Algebra Level 3

I have a Monster, in which when I enter two positive integers \((a,b)\), where \(b>a\), it gives out two positive integers, \((b,a+b)\).

I then enter these two numbers again into the Monster, and get two more numbers.

I do this process continuously \(10\) times, and then add my final two numbers, to get \(3935\).

What is the product of the two numbers I entered at first?

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