#include "perm.h"
#include<bits/stdc++.h>
#define pb push_back
#define fi first
#define se second
#define mp make_pair
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef long double ld;
template <typename T> bool chkmin(T &x,T y){return x>y?x=y,1:0;}
template <typename T> bool chkmax(T &x,T y){return x<y?x=y,1:0;}
ll readint(){
ll x=0,f=1; char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
return x*f;
}
vector<int> primes={2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89};
vector<int> construct_permutation(ll k){
if(k==1) return {};
if(k==2) return {0};
for(int i:primes){
if(i<k&&k%i==0){
vector<int> a=construct_permutation(k/i);
vector<int> b=construct_permutation(i);
for(int i=0;i<(int)b.size();i++) b[i]+=a.size();
vector<int> ret;
for(int i:a) ret.pb(i);
for(int i:b) ret.pb(i);
return ret;
}
}
vector<int> a=construct_permutation(k/2);
a.pb(a.size());
vector<int> ret;
if(k%2==1) ret.pb(a.size());
for(int i:a) ret.pb(i);
return ret;
}
