#include <bits/stdc++.h>
#define pb push_back
#define F first
#define S second
#define debug(x) cout << #x << "= " << x << ", "
#define ll long long
#define fast ios::sync_with_stdio(false), cin.tie(0), cout.tie(0)
#define SZ(x) (int) x.size()
#define wall cout << endl;
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define int long long
string inttostr(int x)
{
int k = 1;
while(k * 2 <= x) k *= 2;
string res;
for(int i = k ; i > 0 ; i >>= 1)
{
if((x & i) != 0) res.pb('1');
else res.pb('0');
}
return res;
}
vector <int> construct_permutation(int k)
{
vector <int> res;
if(k <= 90)
{
for(int i = k - 2 ; i >= 0 ; i--) res.pb(i);
return res;
}
string s = inttostr(k);
int ps;
if(s[1] == '1')
{
res = {1 , 0};
ps = 2;
}
else if(s[2] == '0')
{
res = {2 , 1 , 0};
ps = 3;
}
else
{
res = {1 , 2 , 0};
ps = 3;
}
while(ps < SZ(s))
{
if(ps + 1 == SZ(s))
{
res.pb(SZ(res));
if(s[ps] == '1')
{
for(int i = 0 ; i < SZ(res) ; i++) res[i]++;
res.pb(0);
}
break;
}
else if(s[ps] == '0' && s[ps + 1] == '0')
{
res.pb(SZ(res)); res.pb(SZ(res));
}
else if(s[ps] == '0' && s[ps + 1] == '1')
{
res.pb(SZ(res)); res.pb(SZ(res));
for(int i = 0 ; i < SZ(res) ; i++) res[i]++;
res.pb(0);
}
else if(s[ps] == '1' && s[ps + 1] == '0')
{
res.pb(SZ(res));
for(int i = 0 ; i < SZ(res) ; i++) res[i]++;
res.pb(0); res.pb(SZ(res));
}
else if(s[ps] == '1' && s[ps + 1] == '1')
{
res.pb(SZ(res)); res.pb(SZ(res));
for(int i = 0 ; i < SZ(res) ; i++) if(res[i] > 1) res[i]++;
res.pb(2);
}
ps += 2;
}
return res;
}
