Create a summation method that adds two integers without using any arithmetic operators or built-in addition functions, using bitwise operations.
Implement add_integers(a, b) for signed 32-bit integers. Return their signed 32-bit sum. Do not use +, -, *, /, exponentiation, or built-in addition functions. Handle positive values, negative values, zero, and results that remain within the signed 32-bit range.
def add_integers(a, b):