#include "perm.h"
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define _ << " " <<
#define yes cout<<"YES\n"
#define no cout<<"NO\n"
#define ull unsigned long long
#define lll __int128
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define BlueCrowner ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORD(i, a, b) for (ll i = (a); i >= (b); i--)
const ll mod = 1e9 + 7;
const ll mod1 = 998244353;
const ll naim = 1e9;
const ll max_bit = 60;
const ull tom = ULLONG_MAX;
const ll MAXN = 100005;
const ll LOG = 20;
const ll NAIM = 1e18;
const ll N = 2e6 + 5;
vector<int> construct_permutation(ll k) {
int cur = __lg(k);
vector<int> ans(cur);
iota(all(ans), 0);
FORD(bit, cur - 1, 0) {
if(k & (1ll << bit)) {
ans.insert(ans.begin() + bit, cur);
cur++;
}
}
return ans;
}
