Prior Arbitrary-Scale Image Super-Resolution (ASISR) methods often experience a significant performance decline when the upsampling factor exceeds the range covered by the training data, introducing substantial blurring. To address this issue, we propose a unified model, Stroke-based Cyclic Amplifier (SbCA), for ultra-large upsampling tasks. The key of SbCA is the stroke vector amplifier, which decomposes the image into a series of strokes represented as vector graphics for magnification. Then, the detail completion module also restores missing details, ensuring high-fidelity image reconstruction. Our cyclic strategy achieves ultra-large upsampling by iteratively refining details with this unified SbCA model, trained only once for all, while keeping sub-scales within the training range. Our approach effectively addresses the distribution drift issue and eliminates artifacts, noise and blurring, producing high-quality, high-resolution super-resolved images. Experimental validations on both synthetic and real-world datasets demonstrate that our approach significantly outperforms existing methods in ultra-large upsampling tasks (e.g. $\times100$), delivering visual quality far superior to state-of-the-art techniques.