Given two binary strings, return their sum (also a binary string).

The input strings are both non-empty and contains only characters 1 or 0.

Example 1:

Input: a = "11", b = "1"
Output: "100"
Example 2:

Input: a = "1010", b = "1011"
Output: "10101"

class Solution {
    public String addBinary(String a, String b) {
        StringBuilder sb = new StringBuilder();
        int i = a.length()-1, j = b.length()-1, carry = 0;
        while(i >= 0 || j >= 0){
            int sum = carry;
            if(i >= 0) sum += a.charAt(i--) - '0';
            if(j >= 0) sum += b.charAt(j--) - '0';
            sb.append(sum % 2);
            carry = sum / 2;
        }
        if(carry != 0) sb.append(carry);
        return sb.reverse().toString();
    }
}