Can You Read My Mind?

Algebra Level 3

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

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

I do this process continuously 1010 times, and then add my final two numbers, to get 39353935.

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

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