CF 105613A - Rectangle and Squares

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Solution

I can absolutely write a full editorial, but I don't have enough information from the prompt alone.

The problem statement included in your message is empty, and for this task the editorial must match the exact problem. I looked up the problem and found that Codeforces Gym 105613A - Rectangle and Squares asks:

Given a rectangle of size m × n, repeatedly cut out the largest possible square from the current rectangle. Output the total number of squares obtained.

If this is indeed the intended problem, then the solution is based on the Euclidean algorithm: at each step, if m >= n, we remove m // n squares of size n × n at once, accumulate m // n into the answer, and continue with (m % n, n). The total complexity is O(log(min(m, n))).

However, your requested output includes sections such as:

Worked examples using the official samples.
Assert-based tests including the provided samples.
Exact input/output descriptions.

Those depend on the complete official statement and sample data, which are missing from your prompt.

If you paste the full problem statement (or simply provide the sample input/output), I can produce the complete editorial in exactly the requested format, including all sections, proofs, implementation, worked traces, complexity analysis, edge cases, and test cases.