Hello, relatively new to dynamic programming but I feel it's necessary for me to begin learning it well.

As far as I know, DP depends on storing the solution to previously solved subproblems and reusing them. But in this problem, I do not clearly see how that principle helps to solve this problem. I can only think of a naïve brute force where I try each pair of numbers that sum to s and count them like that.

Could anyone give me a hint as to how to approach thinking about this problem as well as other dynamic programming problems. Thanks in advance for any help.

Edit: I also want to try and avoid the editorial since it usually gives the solution away for me. Just a hint would be appreciated.