#include "perm.h"
#include <cmath>
#include <functional>
#include <fstream>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <list>
#include <time.h>
#include <math.h>
#include <random>
#include <deque>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <sstream>
#include <chrono>
#include <cstring>
#include <numeric>
using namespace std;
typedef long long ll;
int get_nr_bits(ll x)
{
if (x == 0)
{
return 0;
}
assert(x >= 1);
return get_nr_bits(x / 2) + x % 2;
}
vector<int> construct_permutation(ll total)
{
if (total == 1)
{
return {};
}
for (int k = 1; 1; k++)
{
ll rem = total + (k - 1);
int nr_bits = get_nr_bits(rem);
if (k < nr_bits)
{
continue;
}
if (rem & (1LL << 0))
{
continue;
}
// split rem into nr_bits bits
assert(k >= nr_bits);
vector<int> dims;
for (int i = 1; (1LL << i) <= rem; i++)
{
if (rem & (1LL << i))
{
dims.push_back(i);
}
}
int need_extra = k - nr_bits;
for (int i = 0; i < (int)dims.size(); i++)
{
while (dims[i] >= 2 && need_extra > 0)
{
dims.push_back(dims[i] - 1);
dims[i]--;
need_extra--;
}
}
assert(need_extra == 0);
int sumtotal = 0;
for (auto& d : dims)
{
sumtotal += d;
}
vector<int> sol;
for (auto& x : dims)
{
sumtotal -= x;
for (int i = 0; i < x; i++)
{
sol.push_back(sumtotal + i);
}
}
//cout << " : ";
//for (auto& x : sol)
//{
// cout << x << " ";
//}
//cout << "\n";
return sol;
}
return {};
}
