string sum_numbers(string a, string b) {
        char ca, cb, ci, out, co = '0';
        string result = "";
        while (a.size() > 0 || b.size() > 0 || co != '0') {
            ci = co; ca = '0'; cb = '0';
            if (a.size() > 0) {ca = a.back(); a.pop_back();}
            if (b.size() > 0) {cb = b.back(); b.pop_back();}
            result = ((((ca != cb) ? '1' : '0') != ci) ? '1' : '0') + result;
            co = ((((ca == '1' && cb == '1') ? '1' : '0') == '1' || 
                 ((((ca != cb) ? '1' : '0') == '1' && ci == '1') ? '1' : '0') == '1') ? '1' : '0');
        }
        return result;
    }