#include <bits/stdc++.h>
#include <messy.h>
#define taskname "test"
#define fi first
#define se second
#define pb push_back
#define faster ios_base::sync_with_stdio(0); cin.tie(0);
using namespace std;
using ll = long long;
using pii = pair <int, int>;
ll min(const ll &a, const ll &b){
return (a < b) ? a : b;
}
ll max(const ll &a, const ll &b){
return (a > b) ? a : b;
}
const ll Mod = 1000000007;
const int maxN = 1e5 + 1;
int n;
int a[128];
int hiddenarray[] = {3, 1, 7, 4, 5, 0, 6, 2};
vector <string> v;
struct TNode{
vector <int> q;
};
/*
void add_element(string s){
v.pb(s);
}
void compile_set(){
for (string &t: v){
string tt = t;
for (int i = 0; i < n; ++i){
tt[i] = t[hiddenarray[i]];
}
t = tt;
}
}
bool check_element(string s){
for (string t: v){
if (s == t) return 1;
}
return 0;
}*/
void dnc(int l, int r){
if (l == r) return;
int m = (l + r) / 2;
string s = "";
for (int i = 1; i < l; ++i) s += '1';
for (int i = l; i <= r; ++i) s += '0';
for (int i = r + 1; i <= n; ++i) s += '1';
for (int i = l; i <= m; ++i){
s[i - 1] = '1';
add_element(s);
s[i - 1] = '0';
}
dnc(l, m);
dnc(m + 1, r);
}
void dncreturnans(int l, int r, string s){
vector <int> left, right;
for (int i = 0; i < n; ++i){
if (s[i] == '0'){
s[i] = '1';
if (check_element(s)){
left.pb(i);
}
else right.pb(i);
s[i] = '0';
}
}
if (r - l == 1){
a[left[0]] = l - 1;
a[right[0]] = r - 1;
return;
}
int m = (l + r) / 2;
for (int i: right) s[i] = '1';
dncreturnans(l, m, s);
for (int i: right) s[i] = '0';
for (int i: left) s[i] = '1';
dncreturnans(m + 1, r, s);
}
vector <int> restore_permutation(int N, int w, int r){
n = N;
vector <int> b;
dnc(1, n);
compile_set();
string s;
for (int i = 1; i <= n; ++i) s += '0';
dncreturnans(1, n, s);
for (int i = 0; i < n; ++i) b.pb(a[i]);
return b;
}
