DSA Learning Series - Stupid Machine

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Can anyone explain me the approach / methodology of the solution for the question Stupid Machine of DSA Learning Series mentioned below . I wnna know how did he come up to this solution. So that i can also try to think like that which will help me in my DSA learning journey. Since i have been struggling to come up with an optimal solution.Thanks.

Solution of Stupid Machine

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The Editorial describes the approach:

STUPMACH Editorial

PROBLEM LINK: Practice Contest Tester: Roman Bilyi Editorialist: Hussain Kara Fallah PROBLEM EXPLANATION There are N boxes in a line (numbered 1 through N). Initially, the boxes are empty, and I need to use the machine to put tokens in them. For each valid i, the i_{th} box has a maximum capacity S_i tokens. I can perform the following operation any number of times: choose an integer L (1≤L≤N) and put one token in each of the boxes 1,2,…,L. You must put as many tokens as possible into the b…