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We measure the branching fractions B(B+ --> K0bar K+) = (1.61 +/- 0.44 +/- 0.09) * 10^-6 and B(B0 --> K0 K0bar) = (1.08 +/- 0.28 +/- 0.11) * 10^-6, and the CP-violating charge asymmetry A_{CP}(K0bar K+) = 0.10 +/- 0.26 +/- 0.03. 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