A number is called special if when prime factorized as $p1^{a1} * p2^{a2} * ... * pk^{ak}$ , then $a_{i} <= 2$ for all $1 <= i <= k$.

Let $S(N)$ be the sum of all special numbers from $1$ to $N$.

Given $S(10) = 47$ and $S(10^4) = 41586160$

Enter $S(123456789123456789)$ modulo $10^9+7$.