  The reconstruction scheme is developed for modified $f(R)$ gravity with
realistic matter (dark matter, baryons, radiation). Two versions of such theory
are constructed: the first one describes the sequence of radiation and matter
domination, decceleration-acceleration transition and acceleration era and the
second one is reconstructed from exact Lambda-CDM cosmology. The asymptotic
behaviour of first model at late times coincides with the theory containing
positive and negative powers of curvature while second model approaches to
General Relativity without singularity at zero curvature.
