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