[LeetCode] Add Binary

Problem Statement (link):

Given two binary strings, return their sum (also a binary string).
For example,
a = "11"
b = "1"
Return "100".

Analysis:
Starting from end of strings, we add corresponding two digits together. Need to consider the followings:

1) a variable to record if there's carry in each addition;
2) if there's carry when we reach the MSB of two binaries, need to append another digit 1 in front;
3) (option) we could add dummy '0's in front of the shorter string, such that the code is cleaner and easier to understand.

Code:

class Solution {
public:
    string addBinary(string a, string b) {
        string c="";
        int carry=0;
        int al=a.size(), bl=b.size();
        int cl=max(al, bl);

        for (int i=0; i<cl; i++){
            // add dummy 0s in front of shorter string
            int k1=i<al ? a[al-i-1]-'0':0;
            int k2=i<bl ? b[bl-i-1]-'0':0;
            c=to_string((k1+k2+carry)%2)+c;
            carry=(k1+k2+carry)/2;
        }

        // need to check the last carry
        return carry==1 ? "1"+c:c;
    }
};