Siraj Raval and His Dataset

Siraj has a dataset consisting of $N$ 2D cartesian points. Siraj wants to find out a straight line of the form $y = mx$ so that when he takes orthogonal projection of those data points on this line, the average distance of the projected points from the origin is the maximum. As Siraj has got only $5$ minutes to do this, he needs your help in finding out $m$. It can be shown that $m$ can be written in the form $p/q$ where $p$ and $q$ are integers and coprime. You have to find $pq^{-1}$ modulo $10^9+7$.


This is a companion discussion topic for the original entry at https://toph.co/p/siraj-raval-and-his-dataset