#include <bits/stdc++.h>
#define FAST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);cerr.tie(0)
#define mp make_pair
#define xx first
#define yy second
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define all(x) x.begin(),x.end()
#define ff(i,a,b) for (int i = a; i < b; i++)
#define fff(i,a,b) for (int i = a; i <= b; i++)
#define bff(i,a,b) for (int i = b-1; i >= a; i--)
#define bfff(i,a,b) for (int i = b; i >= a; i--)
using namespace std;
long double typedef ld;
unsigned int typedef ui;
long long int typedef li;
pair<int,int> typedef pii;
pair<li,li> typedef pli;
pair<ld,ld> typedef pld;
vector<vector<int>> typedef graph;
unsigned long long int typedef ull;
//const int mod = 998244353;
const int mod = 1000000007;
//Note to self: Check for overflow
#include "perm.h"
vector<int> construct_permutation(li k)
{
if (k<=90)
{
vector<int> ret;
bff(i,0,k-1) ret.pb(i);
return ret;
}
vector<int> p;
li stp=1;
while (2*stp<=k)
{
p.pb((int)p.size());
stp*=2;
}
k-=stp;
int m=(int)p.size();
bff(i,0,m)
{
if (k&(1ll<<i))
{
ff(j,0,(int)p.size()) if (p[j]>=i) p[j]++;
p.pb(i);
}
}
return p;
}
