"""
You are given two input strings, each representing a binary string.

Write a function that returns their sum as a binary string.

The input strings are both non-empty and contains only characters 1 or 0. Additionally, except for the string "0", your inputs will not contain any leading zeroes.

Example 1:

Input: a = "11", b = "1"
Output: "100"

Example 2:

Input: a = "1010", b = "1011"
Output: "10101"
"""
def add_binary(a, b):
    # Your code here

