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