//#include "perm.h"
#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/stack:336777216")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define foru(i, l, r) for(int i = l; i <= r; i++)
#define ford(i, r, l) for(int i = r; i >= l; i--)
#define __TIME (1.0 * clock() / CLOCKS_PER_SEC)
typedef pair<int, int> ii;
typedef pair<ii, int> iii;
typedef pair<ii, ii> iiii;
const int N = 1e6 + 5;
const int oo = 1e9, mod = 1e9 + 7;
void apply_gadget(vector<int>& v,
const vector<int>& gadget) {
vector<int> gadget_items;
for (int x : gadget) if (x > 0) gadget_items.push_back(x);
sort(gadget_items.begin(), gadget_items.end());
for (int x : gadget_items)
for (int& y : v)
if (y >= x) y++;
int n_size = v.size() + gadget.size();
for (int x : gadget) {
if (x <= 0) v.push_back(n_size + x);
else v.push_back(x);
}
}
vector<int> dec2bin(long long int x) {
vector<int> result;
while (x > 0) { result.push_back(x % 2); x /= 2; }
reverse(result.begin(), result.end());
return result;
}
vector<int> permutation(long long int k) {
if (k == 1) return vector<int>();
if (k == 2) return vector<int>({1});
if (k == 3) return vector<int>({2, 1});
vector<int> bin_k = dec2bin(k);
vector<int> result;
int p = 1;
if (bin_k[p] == 0) {
if (bin_k[p + 1] == 0) result = vector<int>({3, 2, 1});
if (bin_k[p + 1] == 1) result = vector<int>({2, 3, 1});
p += 2;
}
else { result = vector<int>({2, 1}); p++; }
while (p + 1 < (int)bin_k.size()) {
if (bin_k[p] == 0) {
apply_gadget(result, vector<int>({0}));
p++;
}
else {
if (bin_k[p + 1] == 0)
apply_gadget(result, vector<int>({ -1, 1, 0}));
else
apply_gadget(result, vector<int>({ -1, 0, 3}));
p += 2;
}
}
if (p < (int)bin_k.size()) {
if (bin_k[p] == 0)
apply_gadget(result, vector<int>({0}));
if (bin_k[p] == 1)
apply_gadget(result, vector<int>({0, 1}));
p++;
}
return result;
}
vector<int> construct_permutation(long long k) {
vector<int> result = permutation(k);
for (int i = 0; i < result.size(); i++)
result[i]--;
return result;
}
/*signed main() {
cin.tie(0)->sync_with_stdio(false);
//freopen(".inp", "r", stdin);
//freopen(".out", "w", stdout);
//process();
cerr << "Time elapsed: " << __TIME << " s.\n";
return 0;
}*/
/*
Xét các trường hợp đặc biệt
Kiểm tra lại input/output
Cố gắng trâu
Lật ngược bài toán
Keep calm and get VOI
Flow:
*/
