Stack problem

#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
ull factorial(ull n);
main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ull n, i, fact[21], j;
    cin>>n;
    stack<ull>num_stack;
//To store factorials upto 20 in the array.
    for(i=0; i<21; i++)
    {
        fact[i]=factorial(i+1);
    }
    for(j=19; j>=0; j--)
    {
        if(fact[j]<=n)
        {
            num_stack.push(j+1);
            n=n-fact[j];
        }
    }
    cout<<num_stack.top()<<' '<<n;

}
ull factorial(ull n)
{//factorial(0)= 1
    if(n==0)
        return 1;
    else
        return n*factorial(n-1);
}