#include "perm.h"
#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define pb push_back
#define vll vector<ll>
#define pll pair<ll, ll>
typedef long long ll;
namespace{
const ll B=2;
vll con;
ll id(ll tar){
return lower_bound(con.begin(), con.end(), tar)-con.begin();
}
}
vector<int> construct_permutation(long long k)
{
vll a;
for(ll rep=0;rep<63-__builtin_clzll(k);rep++){
a.pb(rep*B);
}
k-=(1LL<<(63-__builtin_clzll(k)));
for(ll i=62;i>=0;i--){
if(k&(1LL<<i)){
a.pb((i-1)*B+1);
}
}
con.clear();
for(auto &it:a){
con.pb(it);
}
sort(con.begin(), con.end());
con.erase(unique(con.begin(), con.end()), con.end());
for(ll i=0;i<(ll) a.size();i++){
a[i]=id(a[i]);
}
vector<int> re;
for(auto &it:a){
re.pb(it);
}
return re;
}
