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Reconfigurable intelligent surface (RIS) is a new and revolutionary technology to achieve spectrum-, energy- and cost-efficient wireless networks. This paper studies the resource allocation for RIS-empowered device-to-device (D2D) communication underlaying a cellular network, in which an RIS is employed to enhance desired signals and suppress interference between paired D2D and cellular links. We maximize the overall network's spectrum efficiency (SE) (i.e., sum rate of D2D users and cellular users) and energy efficiency (EE), respectively, by jointly optimizing the resource reuse indicators, the transmit power and the RIS's passive beamforming, under the signal-to-interference-plus-noise ratio constraints and other practical constraints. To solve the non-convex problems, we first propose an efficient user-pairing scheme based on relative channel strength to determine the resource reuse indicators. Then, the transmit power and the RIS's passive beamforming are jointly optimized to maximize the SE by a proposed iterative algorithm, based on the techniques of alternating optimization, successive convex approximation, Lagrangian dual transform and quadratic transform. Moreover, the EE-maximization problem is solved by an alternating algorithm integrated with Dinkelbach's method. Also, the convergence and complexity of both algorithms are analyzed. Numerical results show that the proposed design achieves significant SE and EE enhancements compared to traditional underlaying D2D network without RIS and other benchmarks.