#include<iostream>
#include<vector>
#include<cmath>
#include<set>
#include<string>
#include<sstream>
#include <bits/stdc++.h>
#include "BigIntegerLibrary.hh"


using namespace std;

 string int2string(int n){
    stringstream s;
    s << n; //el numero n passa a ser s
    return(s.str());
}

int main(){
    cout<<"Introduce until which k, n^k: ";
    int mmm;
    cin>>mmm;
    string mm = int2string(mmm);
    BigInteger m = stringToBigInteger(mm);
    cout<<"Introduce until what r, n^k(n+r)!: ";
    int nnn;
    cin>>nnn;
    string nn = int2string(nnn);
    BigInteger n = stringToBigInteger(nn);
    vector<BigInteger> vres;
    vector<vector<BigInteger> > vpol1 (nnn+1);
    vres.push_back(-1);
    string unn;
    BigInteger un = stringToBigInteger(unn);
    un = 1;
    vector<BigInteger> alpha;
    vector<BigInteger> indep;
    string alphanumm;
    BigInteger alphanum = stringToBigInteger(alphanumm);
    string indepnumm;
    BigInteger indepnum = stringToBigInteger(indepnumm);
    string sumafactt;
    BigInteger sumafact = stringToBigInteger(sumafactt);
    sumafact = 0;
    alpha.push_back(1);
    alpha.push_back(0);
    indep.push_back(1);
    indep.push_back(-1);
    vpol1[1].push_back(1);
    vpol1[1].push_back(1);
    vector <vector <BigInteger> > bino (nnn);
    bino[0].push_back(1);
    bino[1].push_back(1);
    bino[1].push_back(1);
    for(unsigned long long int i=2; i<nnn; i++) {
        //cout<<endl<<endl<<1<<"  ";
        bino[i].push_back(1);
        for(unsigned long long int j=1; j<i; j++){
            bino[i].push_back(bino[i-1][j-1]+bino[i-1][j]);
            //cout<<bino[i][j]<<"  ";
        }
        bino[i].push_back(1);
    }
    for(int i=2; i<=mmm; i++){
        alphanum = 0;
        indepnum = 0;
        string ii = int2string(i);
        BigInteger iii = stringToBigInteger(ii);
        vpol1[i].push_back(1);
        //cout<<1<<"  ";
        for(int j=1; j<i; j++){
            string jj = int2string(j);
            BigInteger jjj = stringToBigInteger(jj);
            vpol1[i].push_back(vpol1[i-1][j]+iii*vpol1[i-1][j-1]);
            //cout<<vpol1[i][j]<<"  ";
            alphanum = alphanum + vpol1[i][j]*alpha[i-j];
            indepnum = indepnum + vpol1[i][j]*indep[i-j];
        }
        vpol1[i].push_back(vpol1[i-1][i-1]*i);
        //cout<<vpol1[i-1][i-1]*i<<endl;
        alphanum = alphanum + vpol1[i][i];
        indepnum = indepnum + vpol1[i][i];
        un = un*(iii-1);
        sumafact = sumafact + un;
        //cout<<"alpha: "<<(alpha[0]-alphanum)<<endl;
        alpha.push_back(alpha[0]-alphanum);
        //cout<<"indep: "<<(-indepnum-sumafact)<<endl;
        indep.push_back(-indepnum-sumafact);
    }

    for(int i=2; i<mmm; i++){  //L'EXPONENT
        cout<<endl<<"EXPONENT: "<<i<<endl;
        string ii = int2string(i);
        BigInteger iii = stringToBigInteger(ii);
        for(int k=1; k<nnn; k++){  //LO QUE SE SUMA EN EL FACTORIAL
            //cout<<"se suma al fact: "<<k<<endl;
            vector<vector<BigInteger> > vpol2 (nnn+1);
            vpol2[1].push_back(1);
            vpol2[1].push_back(k);
            for(int w=2; w<=i; w++){  //LES ITERACIONS NECESSĀRIES PER CALCULAR UN POLINOMI DE TAL GRAU FINS i
                vpol2[w].push_back(1);
                //cout<<1<<"  ";      //si vols imprimir el polinomi
                for(int q=1; q<w; q++){
                    vpol2[w].push_back(vpol2[w-1][q]+vpol2[w-1][q-1]*k);
                    //cout<<vpol2[w-1][q]+vpol2[w-1][q-1]*k<<"  ";
                }
                vpol2[w].push_back(vpol2[w-1][w-1]*k);
                //cout<<vpol2[w-1][w-1]*k<<endl;
            }
            //cout<<endl;
            alphanum = 0;
            for(int r=0; r<vpol2[i].size(); r++){
                if(r%2==0){
                    //cout<<"pol: "<<vpol2[i][r]<<endl;
                    //cout<<"alpha corresp: "<<alpha[i-r]<<endl;
                    alphanum = alphanum + vpol2[i][r]*alpha[i-r];
                }
                if(r%2==1){
                    //cout<<"pol: "<<(vpol2[i][r])*(-1)<<endl;
                    //cout<<"alpha corresp: "<<alpha[i-r]<<endl;
                    alphanum = alphanum - (vpol2[i][r])*alpha[i-r];
                }
            }
            cout<<alphanum;
            //cout<<"INDEP: "<<indepnum<<endl;
            cout<<endl;
        }
    }
}