#include "messy.h"
#include <vector>
#include <string>
#include <algorithm>
#include <cassert>
using namespace std;
int N;
void add_strings(int L, int R, string base) {
if(L == R) return;
int mid = (L + R)/2;
for(int i = L; i <= mid; i++) {
base[i] = '1';
add_element(base);
base[i] = '0';
}
base = string(N, '0');
string left = base, right = base;
for(int i = mid + 1; i <= R; i++) left[i] = '1';
for(int i = L; i <= mid; i++) right[i] = '1';
add_strings(L, mid, left);
add_strings(mid + 1, R, right);
}
vector<int> ans_rev;
void solve(int L, int R, vector<int> A, vector<int> other) {
if(L == R) {
assert(A.size() == 1);
ans_rev[L] = A[0];
return;
}
string convert(N, '0');
for(int i: other) convert[i] = '1';
vector<int> left, right;
for(int i: A) {
convert[i] = '1';
if(check_element(convert)) left.push_back(i);
else right.push_back(i);
convert[i] = '0';
}
int mid = (L + R)/2;
solve(L, mid, left, right);
solve(mid + 1, R, right, left);
}
std::vector<int> restore_permutation(int n, int w, int r) {
N = n;
add_strings(0, N - 1, string(N, '0'));
compile_set();
ans_rev.resize(N, -1);
vector<int> A;
for(int i = 0; i < N; i++) A.push_back(i);
solve(0, N - 1, A, {});
vector<int> ans(N);
for(int i = 0; i < N; i++) ans[ans_rev[i]] = i;
return ans;
}
