Represent "N" with "k"

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int main()
{
    ll n,k;
    cin>>n>>k;
    ll x=n;
    ll a[101]={0};
    ll index=0;
    /// this section is the main algo
    while(n)
    {
        ll reminder=n%k;
        n=n/k;
        a[index]+=reminder;
        index++;
    }
    /// this section is used to print values
    for(int i=0;i<101;i++)
    {
        if(a[i]!=0)
        {
            for(int j=0;j<a[i];j++)
                cout<<k<<"^"<<i<<" + ";
        }
    }
    cout<<"0 = "<<x;
}