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A wireless-powered mobile edge computing (MEC) architecture with the cooperation between an access point (AP) and an unmanned aerial vehicle (UAV) is studied in this article. The AP, powered by the grid, is integrated with a high-performance processing server to help compute the user equipment's (UEs') offloaded tasks while also performing high-power laser-like energy charging for the UAV. The UAV serves as (1) an information relay to help the UEs offload/download their computation tasks/results, (2) an energy relay to broadcast energy from the AP to the UEs, as well as (3) an MEC server to help the UEs compute their tasks. We aim at maximizing the weighted sum completed task-input bits (WSCTB) of UEs under the task and time allocation, information-causality, energy-causality, and the UAV's trajectory constraints, by jointly optimizing the task and time allocation as well as the UAV's energy transmit …