Standard Nim
Public  06/24/17  8xp  Math  53.3% 
Let $C(n, k)$ be the number of integer solutions $(x_1, \ldots, x_k)$ such that $\bigoplus_{i=1}^k x_i = 0$ and $0 \le x_i < n$ for each $i$. Here, $x \oplus y$ means $x$ xor $y$.
Let $F(n)$ be the $n$th fibonacci number: $F(0) = 0, F(1) = 1$, and $F(i) = F(i  1) + F(i  2)$ for $i \ge 2$.
Let $$ S(n) := \sum_{i=1}^{n} \sum_{j=1}^{n} C(F(i), F(j)). $$ You are given $S(6) = 2153296$ and $S(7) = 18998620089329$.
Find $S(92)$ modulo $10^9 + 7$.
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