Intuition

Use the identity (a + b)^2 = a^2 + b^2 + 2ab to express ab = ((a+b)^2 - a^2 - b^2) / 2. If direct division is not allowed, compute division by two using a recursive divide_by_2 that subtracts 2 repeatedly.

Approach

Compute val = (a + b)^2 - a^2 - b^2. Then ab = val / 2.
Implement divide_by_2(n) recursively by subtracting 2 until n < 2; count how many times.
Use sign handling to allow negative values of val.

Edge cases: the identity relies on correct squaring and careful handling of large integers; using recursion to divide may be slow and depth-heavy.

Code

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