string addBinary(string a, string b) {
    reverse(a.begin(), a.end());
    reverse(b.begin(), b.end());
    if (a.size() < b.size()) swap(a, b);

    vector<char> res;
    int len = b.size(),minus = a.size()-b.size();
    for (int i = 0; i <len; ++i) {
        res.push_back(b[i] - '0' + a[i]);
    }
    //cout << res << endl;
    for (int i = len; i < len+minus; ++i)
        res.push_back(a[i]);
    /*reverse(res.begin(), res.end());
    cout << res << endl;*/
    //for (auto a : res)
    //  cout << a;
    //cout << endl;
    for (int i = 0; i <len+minus-1; ++i) {
        if (res[i] >= '2') {
            res[i + 1] = res[i + 1] + (res[i] - '0')/2;
            res[i] = '0' + (res[i] -'0') % 2;
        }

        //for (auto a : res)
        //  cout << a;
        //cout << endl;
    }
    //cout << res << endl;
    string result;
    for (auto& a : res)
        result += a;

    //cout << result << endl;

    reverse(result.begin(), result.end());
    if (result[0] > '1') {
        result[0] = result[0] -2;
        result = '1' + result;
    }

    //cout << res << endl;
    //while (res[0] > '1') {
    //  res[0] = res[0] - 2;
    //  res = '1' + res;
    //}
    //reverse(res.begin(), res.end());
    return result;
        
    }