Given two binary strings a and b, return their sum as a binary string. Binary strings contain only the characters '0' and '1'. Do not convert the binary strings to integers - simulate the binary addition directly by processing each string from right to left, tracking the carry at each step.
Examples:
Input: a = '11', b = '1'
Output: '100'
Explanation: 11 (3) + 1 (1) = 100 (4) in binary
Input: a = '1010', b = '1011'
Output: '10101'
Explanation: 1010 (10) + 1011 (11) = 10101 (21) in binary
Input: a = '0', b = '0'
Output: '0'
Explanation: 0 + 0 = 0
Input: a = '1', b = '0'
Output: '1'
Explanation: 1 + 0 = 1
Input: a = '111', b = '111'
Output: '1110'
Explanation: 111 (7) + 111 (7) = 1110 (14) in binary
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