Create an Aurelia component that displays a list of products and allows the user to filter them by availability. The component should have a search input field and a select dropdown that filters the products by "In Stock" or "Out of Stock". Each product in the list should display its name, image, and availability status. The component should have a clean and modern design that is easy to use and visually appealing. In addition, the component should have responsive design and be mobile-friendly.
This prompt doesn't seem malicious.