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Suppose $G \subseteq \mathbb{R}^2$ is dense G-delta. Must there (in ZFC) exist non meager sets of reals $A, B$ such that $A \times B \subseteq G$?

Suppose $G \subseteq \mathbb{R}^2$ is dense $G_\delta$. Must there (in ZFC) exist non meager sets of reals $A, B$ such that $A \times B \subseteq G$?