#include "messy.h"
#include<bits/stdc++.h>
using namespace std;
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ll long long
#define ordered_set tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update>
#define fall(i,a,b) for(int i=a;i<=b;i++)
#define rfall(i,a,b) for(int i=a;i>=b;i--)
#define pb push_back
#define sz(x) (int)x.size()
typedef pair<ll,ll> pii;
int n,cur=1;
vector<int> p,rev;
void build(int l,int r){
if(l==r) return;
int m=(l+r)/2;
if(m<=7) build(m+1,r);
else{
string s="";
fall(i,0,n-1) s+="1";
fall(j,0,cur-2) s[j]='0';
fall(i,l,m){
if(i<=7) continue;
s[i]='0';
add_element(s);
s[i]='1';
}
cur++;
build(l,m);
build(m+1,r);
}
}
void walk(int l,int r,vector<int> v){
if(l==r){
p[v[0]]=l;
rev[l]=v[0];
return;
}
int m=(l+r)/2;
if(m<=7) walk(m+1,r,v);
else{
vector<int> g1,g2;
string s="";
fall(i,0,n-1) s+="1";
fall(j,0,cur-2) s[rev[j]]='0';
for(auto u:v){
s[u]='0';
if(check_element(s)) g1.pb(u);
else g2.pb(u);
s[u]='1';
}
cur++;
walk(l,m,g1); walk(m+1,r,g2);
}
}
std::vector<int> restore_permutation(int N, int lx, int lx2){
n=N;
string s="";
p.resize(n,-1); rev.resize(n);
fall(i,0,n-1) s+="0";
fall(i,0,7){
s[i]='1';
add_element(s);
}
build(0,n-1);
compile_set();
fall(i,0,7) s[i]='0';
fall(j,0,7){
fall(i,0,n-1){
if(p[i]!=-1) continue;
s[i]='1';
if(check_element(s)){
p[i]=j;
rev[j]=i;
break;
}
s[i]='0';
}
}
vector<int> candidates;
fall(i,0,n-1) if(p[i]==-1) candidates.pb(i);
cur=1;
walk(0,n-1,candidates);
return p;
}
