akiran/react-slick ? reverse-engineered prompt

Build me a React carousel component that works like slick carousel, with an easy to use Slider component I can drop into an app and pass settings into. I want it to support the usual things people expect, like dots, infinite looping, speed control, showing one or more slides, and moving by one or more slides at a time. Please include a simple demo page with a few example carousels, and make sure the component is usable in a normal React project without a lot of setup. Also include the styling setup instructions for the slick CSS files, since that seems required for the arrows and dots to look right. If you need to, check the current docs online so the behavior matches the real package. Keep it clean, well tested, and ready to run locally with a basic development setup.