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

For example,
a ="11"
b ="1"
Return"100".

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();
    }
}