// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
#include "messy.h"
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 130;
int n;
vi ans;
void encode(int l, int r, int tl, int tr) {
int m = l + r >> 1;
string s(n, '0');
REP (i, tl, tr) {
s[i] = '1';
}
REP (i, l, m) {
string t = s;
t[i] = '1';
add_element(t);
}
if (l + 1 < r) {
encode(l, m, m, r); encode(m, r, l, m);
}
}
void decode(int l, int r, vi vt, vi id) {
if (l + 1 == r) {
ans[id[0]] = l;
return;
}
int m = l + r >> 1;
string s(n, '0');
for (int i : vt) {
s[i] = '1';
}
vi lv, rv;
for (int i : id) {
string t = s;
t[i] = '1';
if (check_element(t)) {
lv.pb(i);
} else {
rv.pb(i);
}
}
decode(l, m, rv, lv); decode(m, r, lv, rv);
}
vi restore_permutation(int N, int W, int R) {
n = N;
encode(0, n, 0, 0);
compile_set();
vi id(n);
iota(ALL(id), 0);
ans = vi(n);
decode(0, n, vi(), id);
return ans;
}
