class Solution {
public:
    string addBinary(string a, string b) {
         int n1 = a.size() - 1;
        int n2 = b.size() - 1;
        string ret{""};
        bool carry = 0;
        while (n1 >= 0 || n2 >= 0) {
            bool digA = (n1 >= 0) ? a[n1--] - '0' : 0;
            bool digB = (n2 >= 0) ? b[n2--] - '0' : 0;
            bool sum = (digA ^ digB) ^ carry;
            carry = (digA && digB) || ((digA || digB) && carry);
            ret.push_back(sum + '0');
        }
        if (carry) {
            ret.push_back('1');
        }
        reverse(ret.begin(), ret.end());
        return ret;
    }
};