Multiply Without Using Operator

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Problem

Fast Enterprises processes numeric calculations in its Fast platform. Implement integer multiplication without using the multiplication operator or equivalent arithmetic shortcuts.

Given two signed 32-bit integers a and b, return their mathematical product. Your implementation must not use *, /, %, exponentiation, or library functions that directly perform multiplication. Use bit operations, addition, subtraction, and comparisons as needed.

Formal Specification

Input: Two integers a and b, each in the signed 32-bit range.
Output: An integer equal to a × b.
The result may exceed the signed 32-bit range, so return the full mathematical result using Python integers.
The function must terminate in O(log |b|) iterations or better, rather than adding one operand once per unit of the other.

Constraints

-2^31 <= a, b <= 2^31 - 1
The result must be the full mathematical product, even if it exceeds 32-bit range
Do not use multiplication, division, modulo, exponentiation, or direct product helpers
The algorithm must use binary decomposition and finish in O(log |b|) iterations

Function Signature

def multiply_integers(a, b):

Your solutionPython 3

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