#include <bits/stdc++.h>
#include "messy.h"
#ifdef __LOCAL__
#include <debug_local.h>
#endif
using namespace std;
int n;
vector<int> ans;
void insert(int l, int r) {
if (l == r) return;
int m = (l + r) / 2;
string s = string(n, '1');
for (int j = l; j <= r; j++) s[j] = '0';
for (int i = l; i <= m; i++) {
s[i] = '1';
add_element(s);
s[i] = '0';
}
insert(l, m);
insert(m + 1, r);
}
void solve(int l, int r, vector<int> pos) {
if (l == r) {
ans[pos[0]] = l;
return;
}
int m = (l + r) / 2;
string s = string(n, '1');
for (int i : pos) s[i] = '0';
vector<int> mark(n), left, right;
for (int i : pos) {
s[i] = '1';
if (check_element(s)) {
mark[i] = 1;
}
s[i] = '0';
}
for (int i : pos) {
if (mark[i]) left.push_back(i);
else right.push_back(i);
}
solve(l, m, left);
solve(m + 1, r, right);
}
vector<int> restore_permutation(int N, int w, int r) {
n = N;
ans.resize(n);
insert(0, n - 1);
compile_set();
vector<int> a(n);
iota(a.begin(), a.end(), 0);
solve(0, n - 1, a);
return ans;
}
