#include <bits/stdc++.h>
#define endl '\n'
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define fo(i,n) for(auto i =0 ; i < n;i++)
#define fore(i,l,r) for(auto i = l; i < r;i++)
#define forex(i,r,l) for(auto i = r; i >= l; i--)
#define ffo(i,n) forex(i,n-1,0)
#define all(x) x.begin(),x.end()
#define lsb(x) x&(-x)
#define sz(x) (int)x.size()
#define gcd(a,b) __gcd(a,b)
#define vii vector<ii>
using namespace std;
using ll = long long; using ull = unsigned long long;
using vi = vector<int>;using ii = pair<int,int>;using mii = map<int,int>;
// #pragma GCC target ("avx2")
// #pragma GCC optimization ("O3")
// #pragma GCC optimization ("unroll-loops")
vi construct_permutation(ll k){
int act = 0;
vi ans;
while(k>1){
// cout<<k<<endl;cout.flush();
ll lg = 1, p2 = 2;
while(p2*2 <= k)p2*=2, lg++;
vi ins;fo(i,lg)ins.pb(act),act++;
reverse(all(ins));
for(int v : ins)ans.pb(v);
k-=p2;k++;
}reverse(all(ans));
return ans;
}
