Here I am going to present the solution for the first problem from the US Open 2025 USACO Silver Contest, a problem where we can start from a simple construction made of numbers equal to powers of two - 1 and after deducing some extra casework, we can solve all the possible cases depending on parity of m and k.
Solution code: https://usaco-solutions.com/silver/25open-silver-sequence/
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USACO US Open 2025 Silver Problem 1 - Sequence Construction - Solution | NatokHD