How to build a Wordpress form searching posts in a specific category only or sitewide?

How to build a Wordpress form searching posts in a specific category only
or sitewide?

I want to build a Wordpress search from that if somebody selects "Game",
it searches posts in the "Game" category. Or if he/she chooses "The rest
of the site", it searches posts/pages in the site except posts in the
"Game" category. I think radio button is a good option for the selection.
How do I do it? Cheers.