How to connect a program running on my computer to an external web server?

Let's say I want to code a very efficient program (in terms of execution time) in C and to display its output on a specific website; it will be executed everytime a client makes a specific request (i.e. clicking on a button). This program will run on my computer, but its output needs to be sent to the server that hosts this website (and the server is only running Apache). I have read about CGIs, but they are supposed to be outdated and to have very slow time responses, so is there any specific protocol (or anything else) that I should learn for making my aim possible?