Let $f(i)$ denote the $i^{th}$ Fibonacci number ($f(0)=0,f(1)=1$). Based on the given definition, find the value of $S(1234567)$ modulo $1,000,000,007$.

$S(n)=\sum_{i=1}^{n} \sum_{j=0}^{i - 1} \sum_{k=j + 1}^{i} f(i) \cdot f(j) \cdot f(k)$