_{This problem is a programming version of Problem 57 from projecteuler.net}

It is possible to show that the square root of two can be expressed as an infinite continued fraction.

By expanding this for the first four iterations, we get:

The next three expansions are , , and , but the eighth expansion, , is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.

Given . In the first expansions, print the iteration numbers where the fractions contain a numerator with more digits than denominator.