The powerful wavefront manipulation capability of metasurfaces originates from their subwavelength or deep subwavelength elements with designable optical responses, especially phase responses. However, they usually suffer from performance degradation as the spatial phase gradient is large. To solve this issue, we propose an accurate and efficient nonlocal diffraction engineering mechanism to tailor an arbitrary large-gradient wavefront utilizing superwavelength-scale elements. The fast-varying phase profile is cut into segments according to $2\pi$ zones rather than subwavelength discretization. Each phase segment is accurately implemented by precisely tailoring the diffraction pattern of the element, where diffraction angles, efficiencies, and phases are controlled simultaneously. As proof of the concept, high numerical aperture cylindrical metalenses are designed using this method and experimentally validated at the terahertz band. The cylindrical metalens is further extended to a full-space metalens, which enables high-quality subwavelength imaging with resolved details of $0.65\lambda$. The proposed mechanism offers an efficient way to capture the fast-varying wavefront using relatively coarse geometries with new physical insights.