#include <bits/stdc++.h>
#include "messy.h"
using namespace std;
#define pb push_back
vector<int>ans;
int N;
void add(int l,int r,string s){
if(l == r)return;
int mid = (l+r)/2;
for(int i=l;i<=mid;i++){
s[i] = '1';
//cout<<s<<'\n';
add_element(s);
s[i] = '0';
}
s = string(N,'0');
for(int i=mid+1;i<=r;i++)s[i] = '1';
add(l,mid,s);
s = string(N,'0');
for(int i=l;i<=mid;i++)s[i] = '1';
add(mid+1,r,s);
}
void solve(int l,int r,vector<int>v,string s){
if(l==r){
ans[l] = v[0];
return;
}
/*
cout<<l<<" "<<r<<'\n';
for(int x:v)cout<<x<<" ";
cout<<'\n';
cout<<s<<'\n';
*/
vector<int>a,b;
int mid = (l+r)/2;
for(int x:v){
s[x] = '1';
//cout<<s<<" "<<check_element(s)<<'\n';
if(check_element(s))a.push_back(x);
else b.push_back(x);
s[x] = '0';
}
s = string(N,'0');
for(int x:b)s[x] = '1';
solve(l,mid,a,s);
s = string(N,'0');
for(int x:a)s[x] = '1';
solve(mid+1,r,b,s);
//a contains what [l,mid] bijects to in p[l,mid]
//b the inverse
}
vector<int> restore_permutation(int _n, int w, int r) {
int n = _n;
N = _n;
ans.resize(n);
string s(N,'0');
add(0,n-1,s);
compile_set();
vector<int>v(n);
for(int i=0;i<n;i++)v[i] = i;
solve(0,n-1,v,s);
vector<int>p(n);
for(int i=0;i<n;i++)p[ans[i]] = i;
return p;
}
