The inversion count of a sequence of digits is the smallest number of adjacent pairs that must be swapped to sort the sequence.
For example, $34214$ has inversion count of $5$:
$34214 \to 32414 \to 23414 \to 23144 \to 21344 \to12344$.
If each digit of a sequence is replaced by one of its divisors a divided sequence is obtained.
For example, the sequence $332$ has $8$ divided sequences: $\{332,331,312,311,132,131,112,111\}$.
Define $G(N)$ to be the concatenation of all primes less than $N$, ignoring any zero digit.
For example, $G(20) = 235711131719$.
Define $F(N)$ to be the sum of the inversion count for all possible divided sequences from the master sequence $G(N)$.
You are given $F(20) = 3312$ and $F(50) = 338079744$.
Find $F(10^8)$. Give your answer modulo $1\,000\,000\,007$.
solutions/s705.md.