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?