如何计算多项式(x^2^2^2^2 x^2^2^2）

我想计算（x^2^2^2^2 x^2^2^2）结果应该为[x^256 x^16] ..但是我我无法完全做到这一点。我还编写了一个在上半场工作的代码（在' '之前），但在其他一半之前，它无法做到...

#include<iostream>
    #include<string>
    #include <algorithm>
    #include<sstream>
  using namespace std;
  int main()
 {
string a;
cin >> a;
string s1 = "^";
string::size_type foud;
foud = a.find(s1);
int i = foud;
int flag = 0;
i++;
while (foud != std::string::npos)
{
    flag = 0;
    cout << i <<"I"<< endl;
    while (flag != 1 && i < a.length())
    {
        if (a[i] == '(' || a[i] == '+' || a[i] == '-' || a[i] == ')')
        {
            flag++;
            cout << "terminator" << endl;
        }

        else if (a[i] == '^')
        {
            /*int j = (int)(a[i - 1]);
            j = j - 48;
            int k = (int)(a[i + 1]);
            k = k - 48;
            i = k + 1;
            int power =0;
            power = pow(j, k);
            ;*/
            int j = i;
            int k = i;
            k--;
            j++;
            string bcknumber;
            while (a[k] != '^' && a[k] != '(' && a[k] != '+' && a[k] != '-' && a[k] != ')')
            {
                bcknumber = bcknumber + a[k];
                k--;
            }
            cout << bcknumber << endl;
            reverse(bcknumber.begin(), bcknumber.end());
            cout << bcknumber << endl;
            int BK;
            BK = stoi(bcknumber);
            int FD;
            string frdnum;
            while (a[j] != '^'&&a[j] != '' && a[j] != '(' && a[j] != '+' && a[j] != '-' && a[j] != ')')
            {
                frdnum = frdnum + a[j];
                j++;
            }
            FD = stoi(frdnum);
            int resil = pow(BK, FD);
            frdnum.clear();
            stringstream s;
            string res;
            s << resil;
            res = s.str();
            if (i == 15)
            {
                a.replace(14, 15, res);
            }
            else
            {
                a.replace(i - bcknumber.length(), i + frdnum.length(), res);
            }
            i--;
            bcknumber.clear();

        }
        else
            i++;
    }
    foud = a.find("^", foud + 1);
    i = foud;
    i++;

}
cout << a << endl;
system("pause");
 }