The advancements in image super-resolution technology have led to its widespread use in remote sensing applications. However, there is currently a lack of a general solution for the reconstruction of satellite images at arbitrary resolutions. The existing scale-arbitrary super-resolution methods are primarily predicated on learning either a discrete representation (DR) or a continuous representation (CR) of the image, with DR retaining the sensitivity to resolution and CR guaranteeing the generalization of the model. In this paper, we propose a novel image representation that combines the discrete and continuous representation, known as CDCR, which enables the extension of images to any desired resolution in a plug-and-play manner. CDCR consists of two components: a CR-based dense prediction that gathers more available information and a DR-based resolution-specific refinement that adjusts the predicted values of local pixels. Furthermore, we introduce a scale cumulative ascent (SCA) method, which enhances the performance of the dense prediction and improves the accuracy of the generated images at ultra-high magnifications. The efficacy and dependability of CDCR are substantiated by extensive experiments conducted on multiple remote sensing datasets, providing strong support for scenarios that require accurate images.