Consider all points with integral positive coordinate $(x,y)$ which lies on the curve

Let $P_i$ be the coordinate of $i^{th}$ point when all the points satisfying above equation are sorted in ascending order according to their distance from the origin.

Let $D_i$ = distance between (0,0) and $Pi$

If $S(n)$ =$\sum_{i=1}^{n}$ $Di^2$

Enter the value of $S(10^{15}) mod 1000000009$.