class Solution {

    public String addBinary(String a, String b) {

        int ptrA = a.length()-1;

        int ptrB = b.length()-1;

        int jwz = 0;

        String sum = "";

        while(ptrA>=0&&ptrB>=0)

        {

            int val = (a.charAt(ptrA)-'0')+(b.charAt(ptrB)-'0')+jwz;

            if(val==2){

                sum="0"+sum;

                jwz=1;

            }

            else if(val==3)

            {

                sum="1"+sum;

                jwz=1;

            }

            else{

                sum=val+sum;

                jwz=0;

            }

            ptrA--;

            ptrB--;

        }

        while(ptrA>=0){

            int val = (a.charAt(ptrA--)-'0')+jwz;

            if(val==2)

            {

                sum="0"+sum;

                jwz=1;

            }

            else{

                sum=val+sum;

                jwz=0;

            }

        }

         while(ptrB>=0){

            int val = (b.charAt(ptrB--)-'0')+jwz;

            if(val==2)

            {

                sum="0"+sum;

                jwz=1;

            }

            else{

                sum=val+sum;

                jwz=0;

            }

        }

        if(jwz==1)

            sum='1'+sum;

        return sum;

    }

}