A search for the lepton-flavour violating decays $B^+ to K^+ {mu}^{pm} e^{mp}$ is performed using a sample of proton-proton collision data, collected with the LHCb experiment at centre-of-mass energies of $7$ and $8~{rm TeV}$ and corresponding to an integrated luminosity of 3$rm~fb^{-1}$. No significant signal is observed, and upper limits on the branching fractions are set as $mathcal{B}(B^+ to K^+ {mu}^- e^+) < 7.0~(9.5) times 10^{-9}$ and $mathcal{B}(B^+ to K^+ {mu}^+ e^-) < 6.4~(8.8) times 10^{-9}$ at 90 (95) % confidence level. The results improve the current best limits on these decays by more than one order of magnitude.
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