A system consists of N identical particles of mass m placed rigidly on the vertices of a regular polygon with each side of length 'a '. If $k_1$ be the kinetic energy imparted to one of the particles so that it just escapes the gravitational pull of the system and  thereafter kinetic energy $k_2$ is given by to the adjacent particle to escape, then the difference $(k_1-k_2)$ is $\frac{{\text{Gm}}^2}{pa}$ then p is