CF 102576B - Binomial

CF 102576B - Binomial

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Solution

The problem statement in your prompt is corrupted. The mathematical expression that defines the condition is missing because the PDF text extraction failed.

It currently appears as:

find the number of pairs (i, j) such that aaji is odd.

The missing expression is the entire problem. Without knowing whether it is asking about something like

• $\binom{a_i}{a_j}$,
• $\binom{a_j}{a_i}$,
• $a_i^{a_j}$,
• $a_j^{a_i}$,

or another formula entirely, it is impossible to derive the correct algorithm, prove correctness, or produce working code.

A complete editorial would necessarily depend on the exact mathematical property being tested. For example, if the problem is about the parity of a binomial coefficient $\binom{a_i}{a_j}$, the solution uses Lucas' theorem over modulo 2 and bitwise subset tests. If it is a different expression, the solution is completely different.

Please provide one of the following:

1. The original PDF or image of the statement.
2. The Codeforces link.
3. The exact missing mathematical expression (for example, "count pairs where $\binom{a_i}{a_j}$ is odd").

Once I have the correct statement, I can write the full editorial exactly in the requested format, including the proof, optimal algorithm, Python implementation, worked examples, complexity analysis, edge cases, and test cases.