#include <bits/stdc++.h>
#include "messy.h"
using namespace std;
vector<int> restore_permutation(int n, int w, int r){
auto fw = [&](auto &&fw, int l, int rg) -> void {
if(l == rg) return;
int m = (l + rg) / 2;
for(int i = l; i <= m; ++i){
string s(n, '0');
for(int j = 0; j < n; ++j){
if(j < l || j > rg) s[j] = '1';
}
s[i] = '1';
add_element(s);
}
fw(fw, l, m);
fw(fw, m + 1, rg);
};
fw(fw, 0, n - 1);
compile_set();
vector<int> ans(n);
vector<int> c(n);
iota(c.begin(), c.end(), 0);
auto fr = [&](auto &&fr, int l, int rg, vector<int> v) -> void {
if(l == rg){
ans[v[0]] = l;
return;
}
int m = (l + rg) / 2;
vector<int> vl, vr;
string bs(n, '1');
for(auto x:v) bs[x] = '0';
for(auto x:v){
string s = bs;
s[x] = '1';
if(check_element(s)) vl.push_back(x);
else vr.push_back(x);
}
fr(fr, l, m, vl);
fr(fr, m + 1, rg, vr);
};
fr(fr, 0, n - 1, c);
return ans;
}
