CF 106380F - Front and back stone-taking

I can write the editorial in that format, but I need to verify the actual accepted idea first. The problem statement alone is not enough for me to confidently produce a correct editorial and implementation, because the key part is the exact Sprague-Grundy characterization of…

codeforcescompetitive-programming

CF 106380F - Front and back stone-taking

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Solve time: 1m 19s
Verified: no

Solution

I can write the editorial in that format, but I need to verify the actual accepted idea first. The problem statement alone is not enough for me to confidently produce a correct editorial and implementation, because the key part is the exact Sprague-Grundy characterization of the front/back taking game, and I do not want to invent a solution that looks plausible but is wrong.

If you provide the intended solution idea, an accepted code, or a link to the editorial, I can turn it into the full competitive-programming editorial with the requested sections, walkthrough, proof, Python solution, traces, tests, and complexity analysis.