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

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

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class Solution
{
public:
    string addBinary(string a, string b)
    {
        string result = "";
        
        int sum = 0, i = a.length() - 1, j = b.length() - 1;
        while(i >= 0 || j >= 0 || sum == 1)
        {
            sum += i >= 0 ? a[i --] - '0' : 0;
            sum += j >= 0 ? b[j --] - '0' : 0;
            result = char(sum % 2 + '0') + result;
            sum /= 2;
        }
        
        return result;
    }
};