CF 103414H - Octopus Game

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Solve time: 33s
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Solution

I’m missing the actual core of the task statement in your prompt, and without it I can’t produce a correct Codeforces editorial. The page I can access only shows the problem title and samples, not the full rules in a reliable structured way.

From the snippet, I can see this is the classic “Octopus Game” where you start with two integers and repeatedly apply operations of the form:

You pick an integer k, then either replace a with a + k·b or replace b with b + k·a. The goal is to reach a state where one of the numbers becomes zero in at most 50 operations, while keeping values within ±1e18.

But the missing part is crucial: the intended construction strategy depends heavily on whether the official solution uses something like Euclid-style reduction, continued fractions, or bounded coefficient control, and different editorial structures would be wrong without confirming that.

Please paste the full problem statement (or confirm it matches exactly the standard Octopus Game from SpbKOSHP 2021 / CF Gym 103414H), and I’ll write the complete editorial in the format you requested, including full algorithm, correctness argument, implementation details, and test cases.