#include "messy.h"
#include <bits/stdc++.h>
using namespace std;
int n;
vector<int> ans;
void solve(int l, int r){ //we can do recursion!
if(l == r) return;
int mid = (l+r)>>1;
string s;
for(int i = 0;i<n;++i){
s += '0';
}
for(int i = l;i<=r;++i){
s[i] = '1';
}
for(int i = mid+1;i<=r;++i){
s[i] = '0';
add_element(s);
cout << s << "\n";
s[i] = '1';
}
solve(l,mid); solve(mid+1,r);
}
void read(int l, int r, vector<int> v){
if(l == r){
ans[v[0]] = l;
return;
}
int mid = (l+r)>>1;
string s;
for(int i = 0;i<n;++i){
s += '0';
}
for(auto x : v){
s[x] = '1';
}
vector<int> low, high;
for(auto x : v){
s[x] = '0';
if(check_element(s)){
high.push_back(x);
}
else{
low.push_back(x);
}
s[x] = '1';
}
read(l,mid,low); read(mid+1,r,high);
}
vector<int> restore_permutation(int N, int w, int r){
n = N; ans = vector<int>(N);
solve(0,N-1);
vector<int> v;
for(int i = 0;i<N;++i){
v.push_back(i);
}
read(0,N-1,v);
return ans;
}
