We first introduce the (on the fly) Heat Bath excitation generator which calculates matrix elements to all connected determinants on the fly and suggests a new determinant with proportional probability. From the generation probabilities standpoint this is the ideal excitation generator, but the wall clock time per excitation becomes quickly large because on the fly calculation of matrix elements incurs large overheads and the setup of the non uniform probability distributions scales with the number of orbitals n and number of particles N as