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

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

public class AddBinary {
    public String addBinary(String a, String b) {
        StringBuilder result = new StringBuilder();
        
        int carry = 0;
        int i = a.length() - 1;
        int j = b.length() - 1;
        
        while(i >= 0 || j >= 0) {
            int sum = carry;

            if(i >= 0) {
                sum += a.charAt(i--) - '0';
            }

            if(j >= 0) {
                sum += b.charAt(j--) - '0';
            }

            result.append(sum % 2);
            carry = sum / 2;
        }

        if(carry != 0) {
            result.append(carry);
        }

        return result.reverse().toString();
    }
}