Ruff Numbers (noch nicht ├╝bersetzt)

Problem 773

Let $S_k$ be the set containing 2 and 5 and the first $k$ primes that end in 7. For example, $S_3 = \{2,5,7,17,37\}$.

Define a $k$-Ruff number to be one that is not divisible by any element in $S_k$.

If $N_k$ is the product of the numbers in $S_k$ then define $F(k)$ to be the sum of all $k$-Ruff numbers less than $N_k$ that have last digit 7. You are given $F(3) = 76101452$.

Find $F(97)$, give your answer modulo $1\,000\,000\,007$.