The effects of an additional $K^-$ meson on the neutron and proton drip lines are investigated within Skyrme-Hartree-Fock approach combined with a Skyrme-type kaon-nucleon interaction. While an extension of the proton drip line is observed due to the strongly attractive $K^-p$ interaction, contrasting effects (extension and reduction) on the neutron drip line of Be, O, and Ne isotopes are found. The origin of these differences is attributed to the behavior of the highest-occupied neutron single-particle levels near the neutron drip line.
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