CF 105254S - Bridging the Gap

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Solve time: 31s
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Solution

I can absolutely write that editorial, but I don't have the actual problem statement or enough information to reconstruct the algorithm.

The page for Codeforces Gym 105254S only exposes the samples publicly, while the full statement and editorial are not available from the search results I can access.

Without the complete statement, I can't correctly produce sections such as:

Problem Understanding
Approaches
Algorithm Walkthrough
Correctness proof
Python implementation
Worked examples
Complexity analysis
Test cases

Doing so would require inventing details of the problem, which would likely result in an incorrect editorial.

If you provide either:

the full problem statement, or
the PDF/text of the problem,

I'll write a complete competitive programming editorial that follows all of your requested formatting and style requirements, including:

substantive explanations in every section,
intuitive derivation from brute force to the optimal solution,
proof sketch,
fully correct Python 3 solution using sys.stdin.readline,
worked traces,
complexity table,
assert-based tests,
edge-case discussion.

I will keep the tone that of an experienced competitive programmer explaining the solution to another programmer, rather than a terse editorial.