Parton shower algorithm with the saturation effect

We extend the previously developed small -x parton shower algorithm to include the kinematic constraint effect and kt resummation effect. This work enables the Monte Carlo generator to simultaneously resum large-kt and small -x logarithms in the saturation regime for the first time. It is an important step towards simulating processes involving multiple well separated hard scales, such as dijet production in eA collisions at the EIC.