  We present an algorithm of quantum engineering of large-amplitude>5
high-fidelity>0.99 even/odd Schrodinger cat states (SCSs) using a single mode
squeezed vacuum (SMSV) state as resource. Set of k beam splitters (BSs) with
arbitrary transmittance and reflectance coefficients sequentially following
each other acts as a hub that redirects a multiphoton state into the measuring
modes simultaneously measured by photon number resolving (PNR) detectors. We
show that the multiphoton state splitting guarantees significant increase of
the success probability of the cat state generator compared to its
implementation in a single PNR detector version and imposes less requirements
on ideal PNR detectors. We prove that the fidelity of the output SCSs and its
success probability are in conflict with each other (which can be quantified)
in a scheme with ineffective PNR detectors, especially when subtracting large
(say, 100) number of photons, i.e., increasing the fidelity to perfect values
leads to a sharp decrease in the success probability. In general, the strategy
of subtracting up to 20 photons from initial SMSV in setup with two BSs is
acceptable for achieving sufficiently high values of the fidelity and success
probability at the output of the generator of the SCSs of amplitude <3 with two
inefficient PNR detectors.
