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We present a search for the rare decays B+ -> K+ nu nubar and B0 -> K0 nu nubar
using 459 million BBbar pairs collected with the BaBar detector
at the SLAC National Accelerator Laboratory.
Flavor-changing neutral-current decays such as these are forbidden at tree level
but can occur through one-loop diagrams in the Standard Model (SM), with possible contributions from new physics at the same order.
The presence of two neutrinos in the final state makes identification of
signal events challenging, so reconstruction in
the semileptonic decay channels B -> D(*) l nu of the B meson recoiling from the signal B is used to suppress backgrounds.
We set an upper limit at the 90% confidence level of 1.3 x 10^{-5} on the total branching fraction for B+ -> K+ nu nubar,
and 5.6 x 10^{-5} for B0 -> K0 nu nubar. We additionally report partial branching fractions in two ranges
of di-neutrino mass squared for B+ -> K+ nu nubar.
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