Houraisan☆Kaguya is the princess who lives in Literally House of Eternity. However, she is very playful and often stays up late. This morning, her tutor, Eirin Yagokoro was going to teach her some knowledge about the Fibonacci sequence. Unfortunately, the poor princess was so sleepy in class that she fell asleep. Angry Eirin asked her to complete the following task:
This sequence can be described by following equations:
1.F[1]=F[2]=1
2.F[n]=F[n-1]+F[n-2] (n>2)
Now, Kaguya is required to calculate F[k+1]*F[k+1]-F[k]*F[k+2] for each integer k that does not exceed 10^18.
Kaguya is so pathetic. You have an obligation to help her.
(I love Houraisan Kaguya forever!!!)