#include "perm.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
const long long INF = 1e17;
typedef long long ll;
const ll MOD = 998244353;
#define F first
#define pb push_back
#define S second
#define P pair
#define V vector
#define all(v) v.begin(), v.end()
int mx(ll n) {
int maxd=0;
for (int i=0;i<60;i++) {
if (((1LL<<i)&n)!=0) {
maxd=i;
}
}
return maxd;
}
std::vector<int> construct_permutation(long long k)
{
k--;
if (k==1) {
return {0};
}
int id=mx(k);
V<int>vp;
int g=0;
for (int i=0;i<id;i++) {
vp.pb(i+g);
if (((1LL<<(i+1))&k)!=0 && i+1!=id) {
g++;
}
}
int num=1;
if ((k&1)!=0) {
num++;
}
for (int i=id-1;i>=1;i--) {
if (((1LL<<i)&k)!=0) {
vp.pb(vp[i-1]+1);
}
}
for (auto &u:vp) {
u+=num;
}
for (int i=num-1;i>=0;i--) {
vp.pb(i);
}
return vp;
}
