#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<vi>;
using vvi = V<vi>;
#include "perm.h"
vi construct_permutation(long long k)
{
int l = __lg(k), x = l;
vi A(l);
iota(all(A), 0);
for (int i = l-1; i >= 0; --i) if ((k >> i) & 1) A.insert(A.begin()+i, x++);
return A;
}
