en.javascript.info/2-ui/4-forms-controls/2-focus-blur/5-keyboard-mouse/solution.md

We can use mouse.onclick to handle the click and make the mouse "moveable" with position:fixed, then then mouse.onkeydown to handle arrow keys.

The only pitfall is that keydown only triggers on elements with focus. So we need to add tabindex to the element. As we're forbidden to change HTML, we can use mouse.tabIndex property for that.

P.S. We also can replace mouse.onclick with mouse.onfocus.