Let's consider about "Fibonacci Numbers". It looks like Problem 2, but it's difficult more than Problem 2.
Let $F_n =
\begin{cases}
1 & n=0 \\
2 & n=1 \\
F_{n1}+F_{n2} & n \ge 2
\end{cases}$
So, the sequence $F_i = 1,2,3,5,8,13,21,34,55,89,144,233,...$
By considering the terms in the Fibonacci sequence whose values do not exceed $10^{10^{13}}$, find the sum of the evenvalued terms modulo $10^9+7$.
Even Fibonacci Numbers 2

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