#include "messy.h"
//#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
#define debug(s) cout<< #s <<" = "<< s <<endl
#define all(v) (v).begin(), (v).end()
#define KeepUnique(v) (v).erase( unique(all(v)), v.end() )
#define MEMSET(a,val) memset(a, val, sizeof a)
#define PB push_back
#define endl '\n'
inline int myrand(int l, int r) {
int ret = rand(); ret <<= 15; ret ^= rand();
if(ret < 0) ret = -ret; ret %= (r-l+1); ret += l;
return ret;
}
template <typename F, typename S>
ostream& operator << (ostream& os, const pair< F, S>& p) {
return os<<"(" <<p.first<<", "<<p.second<<")"; }
typedef pair<int, int> ii;
template<typename T> using min_pq =
priority_queue<T, vector<T>, greater<T> >;
//int dx[] = {-1, +0, +1, +0};
//int dy[] = {+0, +1, +0, -1};
int n;
vector<int> ans;
void add(int b, int e) {
if(b == e) return;
string s(n, '1');
int mid = b + e >> 1;
for(int i = b; i <= e; i++) s[i] = '0';
for(int i = b; i <= e; i++) s[i] = '0';
for(int i = b; i <= (b + e) / 2; i++) {
s[i] = '1', add_element(s), s[i] = '0';
} add(b, mid), add(mid + 1, e);
}
void solve(int b, int e, vector<int> sub) {
if(b == e) assert(sub.size() == 1);
if(b == e) return void(ans[sub[0]] = b);
int mid = b + e >> 1;
string s(n, '1');
for(int i : sub) s[i] = '0';
vector<int> subleft, subright;
for(int i : sub) {
s[i] = '1';
if(check_element(s)) subleft.push_back(i);
else subright.push_back(i);
s[i] = '0';
}
solve(b, mid, subleft), solve(mid + 1, e, subright);
}
vector<int> inverse(vector<int> p) {
vector<int> tmp(p.size());
for(int i = 0; i < p.size(); i++) {
tmp[i] = p[p[i]];
} return tmp;
}
vector<int> restore_permutation(int N, int w, int r) {
n = N;
ans.resize(n);
add(0, n - 1);
compile_set();
vector<int> tmp;
for(int i = 0; i < n; i++)
tmp.push_back(i);
solve(0, n - 1, tmp);
return ans;
}
