A free falling, absorbing liquid drop hit by a nanosecond laser pulse experiences a strong recoil pressure kick. As a consequence, the drop propels forward and deforms into a thin sheet which eventually fragments. We study how the drop deformation depends on the pulse shape and drop properties. We first derive the velocity field inside the drop on the time scale of the pressure pulse, when the drop is still spherical. This yields the kinetic energy partition inside the drop, which precisely measures the deformation rate with respect to the propulsion rate, before surface tension comes into play. On the time scale where surface tension is important, the drop has evolved into a thin sheet. Its expansion dynamics is described with a slender-slope model, which uses the impulsive energy partition as an initial condition. Completed with boundary integral simulations, this two-stage model explains the entire drop dynamics and its dependence on the pulse shape: for a given propulsion, a tightly focused pulse results in a thin curved sheet which maximizes the lateral expansion, while a uniform illumination yields a smaller expansion but a flat symmetric sheet, in good agreement with experimental observations.