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A binned Dalitz plot analysis of $B^\pm \to D K^\pm$ decays, with $D \to K_S\pi^+\pi^-$ and $D \to K_S K^+ K^-$, is performed to measure the \CP-violatingobservables $x_{\pm}$ and $y_{\pm}$, which are sensitive to theCabibbo-Kobayashi-Maskawa angle $\gamma$. The analysis exploits a sample ofproton-proton collision data corresponding to 3.0\invfb collected by the LHCbexperiment. Measurements from CLEO-c of the variation of the strong-interactionphase of the $D$ decay over the Dalitz plot are used as inputs. The values ofthe parameters are found to be $x_+ = (-7.7 \pm 2.4 \pm 1.0 \pm 0.4)\times10^{-2}$, $x_- = (2.5 \pm 2.5 \pm 1.0 \pm 0.5) \times 10^{-2}$, $y_+ = (-2.2\pm 2.5 \pm 0.4 \pm 1.0)\times 10^{-2}$, and $y_- = (7.5 \pm 2.9 \pm 0.5 \pm1.4) \times 10^{-2}$. The first, second, and third uncertainties are thestatistical, the experimental systematic, and that associated with theprecision of the strong-phase parameters. These are the most precisemeasurements of these observables and correspond to $\gamma =(62^{\,+15}_{\,-14})^\circ$, with a second solution at $\gamma \to \gamma +180^\circ$, and $r_B = 0.080^{+ 0.019}_{-0.021}$, where $r_B$ is the ratiobetween the suppressed and favoured $B$ decay amplitudes.

Measurement of the CKM angle \gamma using B^\pm --> D K^\pm with D-->K_S\pi^+\pi^-, K_SK^+K^- decays