High Not Score

The Futility Closet posted a nice problem, http://www.futilitycloset.com/2015/12/16/hard-target/. In a game where you can score 3 points and 7 points only, what is the highest score you can not get. (The high not score?) It was fun to think about, with great connections to combinations, diophantine equations and primes, so I wanted to make a visualization. And then a generalization, because why should 3 and 7 have all the fun? So what's the answer for 3 and 7? For a general s1 and s2?