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();

    }

}