#include "perm.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> construct_permutation(long long k)
{
vector<int> binary;
while (k) {
binary.push_back(k & 1);
k >>= 1;
}
reverse(binary.begin(), binary.end());
deque<int> dq;
int cnt = 0, sz = (int)binary.size(), cntt = 0;
for (int i = 1; i < sz; ++i) {
dq.emplace_back(cnt++);
if (binary[i]) {
if (i + 1 < sz and binary[i + 1] and cntt > 1) {
dq.emplace_back(cnt++);
dq.insert(dq.begin() + 2, cnt++);
++i;
}
else dq.emplace_front(cnt++), cntt++;
}
}
return {dq.begin(), dq.end()};
}
