Hi everyone, I was able to think the solution for E. Cyclic Balance, but the $$$O(1)$$$ constraints in the editorial specifically $$$K \ge \lceil (L_0 + L_1 - c) / 3 \rceil$$$ felt like magic. I wanted to see if I could derive this exact formula from first principles without relying on combinatorial guessing. I hope this perspective helps someone else too.