project euler problem 435

Polynomials of Fibonacci numbers

This problem is relatively simple. But a little bit math is required to avoid computer to do huge amount of work. This problem is very similar to some older problem. You may first  ask yourself a simpler question, how to calculate the 10^15th Fibonacci number(mod n)? 

 After I get the answer for F_7(11) correct. I immediately get the correct solution for the problem. The only bad thing is that I used some sort of bigInteger in my code, but it may not be necessary if you handle the problem in a different approach.