#include "messy.h"
#include <bits/stdc++.h>
using namespace std;
#define name "code"
#define MAXN 1003
#define pb push_back
#define pf push_front
#define ll long long
#define ii pair<int, int>
#define fs first
#define sc second
#define ill pair<int, ll>
#define lli pair<ll, int>
#define llll pair<ll, ll>
#define all(v) v.begin(),v.end()
#define uni(v) v.erase(unique(all(v)),v.end())
#define bit(n,i) (((n)>>(i))&1)
#define FOR(i,a,b) for (int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for (int i=(a),_b=(b); i>=_b; i--)
#define MASK(i) (1LL<<(i))
const int INF=1e9;
const int MOD=1e9+7;
void add(int &u, int v){
u+=v;
if (u>=MOD) u-=MOD;
}
void sub(int &u, int v){
u-=v;
if (u<0) u+=MOD;
}
void minimize(int &u, int v){
u=min(u,v);
}
void maximize(int &u, int v){
u=max(u,v);
}
long long Rand(long long l, long long r){
ll tmp=0;
FOR(i,1,4) tmp=((tmp<<15)^(((1<<15)-1)&rand()));
return l+tmp%(r-l+1);
}
string tmp;
vector<string> writes,reads;
void dnc(int l, int r){
if (l==r) return;
int mid=(l+r)/2;
FOR(i,l,r) tmp[i-1]='0';
FOR(i,l,mid){
tmp[i-1]='1';
writes.pb(tmp);
tmp[i-1]='0';
}
FOR(i,l,r) tmp[i-1]='1';
dnc(l,mid);
dnc(mid+1,r);
}
vector<int> v1,v2;
vector<int> kq;
void solve(int l, int r, vector<int> vec){
if (l==r){
if ((int)vec.size()==0){
return;
}
//cerr<<vec[0]-1<<" "<<l-1<<"\n";
kq[vec[0]-1]=l-1;
return;
}
int mid=(l+r)/2;
v1.clear();
v2.clear();
for (int x:vec){
tmp[x-1]='0';
}
for (int x:vec){
tmp[x-1]='1';
if (check_element(tmp)) v1.pb(x);
else v2.pb(x);
tmp[x-1]='0';
}
for (int x:vec) tmp[x-1]='1';
/*
cout<<l<<" "<<r<<"->"<<"\n";
for (int x:v1) cout<<x-1<<" ";
cout<<"\n";
for (int x:v2) cout<<x-1<<" ";
cout<<"\n\n";
*/
solve(l,mid,v1);
solve(mid+1,r,v2);
}
vector<int> restore_permutation(int n, int w, int r){
tmp="";
FOR(i,1,n) tmp+="0";
FOR(i,1,(int)n/2){
tmp[i-1]='1';
writes.pb(tmp);
tmp[i-1]='0';
}
FOR(i,1,n) tmp[i-1]='1';
dnc(1,(int)n/2);
dnc((int)n/2+1,n);
for (string &x:writes) add_element(x);
compile_set();
FOR(i,1,n) tmp[i-1]='0';
vector<int> vec1,vec2;
FOR(i,1,n){
tmp[i-1]='1';
if (check_element(tmp)){
//cout<<tmp<<"\n";
vec1.pb(i);
}
else vec2.pb(i);
tmp[i-1]='0';
}
FOR(i,1,n) tmp[i-1]='1';
/*
cout<<1<<" "<<n<<"->"<<"\n";
for (int x:vec1) cout<<x-1<<" ";
cout<<"\n";
for (int x:vec2) cout<<x-1<<" ";
cout<<"\n\n";
*/
kq.resize(n,0);
solve(1,(int)n/2,vec1);
solve((int)n/2+1,n,vec2);
return kq;
}
