1103 integer factorization

#include <vector>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <numeric>
using namespace std;
class sol{
public:
    vector<int> seq;
    int sum;
};
bool operator<(const sol& a,const sol& b){
    if(a.sum != b.sum)
        return a.sum > b.sum;
    else{
        for(int i = 0;i < a.seq.size();i++){
            if(a.seq[i] < b.seq[i])
                return false;
            else if(a.seq[i] > b.seq[i])
                return true;
        }
    }
}
void rec(vector<int>& pvec,vector<sol>& ret,sol seq,int n,int k,int p,int id){
    if(n < k || k == 0 && n != 0 || n > k * pvec[id])
        return;
    else if(n == 0 && k == 0){
        seq.sum = accumulate(seq.seq.begin(),seq.seq.end(),0);
        ret.push_back(seq);
    }
    else{
        int root(pvec.size() - 1);
        for(int i = id;i >= 1;i--){
            int tmp(pvec[i]);
            if(n >= tmp + k - 1){
                seq.seq.push_back(i);
                rec(pvec,ret,seq,n - tmp,k-1,p,i);
                seq.seq.pop_back();
            }
        }
    }
}
int main(){
    int n,k,p;
    scanf("%d %d %d",&n,&k,&p);
    vector<sol> ret;
    sol seq;
    vector<int> pvec;
    int num(0);
    while(true){
        int tmp(pow(float(num),p));
        if(tmp <= n){
            pvec.push_back(tmp);
        }
        else{
            break;
        }
        num++;
    }
    int id(pvec.size() - 1);
    rec(pvec,ret,seq,n,k,p,id);
    if(ret.size() == 0)
        printf("Impossible\n");
    else{
        sort(ret.begin(),ret.end());
        printf("%d = ",n);
        for(int i = 0;i < k;i++){
            if(i == 0){
                printf("%d^%d",ret[0].seq[0],p);
            }
            else{
                printf(" + %d^%d",ret[0].seq[i],p);
            }
        }
        printf("\n");
    }
    return 0;
}