#include<bits/stdc++.h>
using namespace std;
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define FORD(i, a, b) for (int i = (a), _b = (b); i >= _b; i--)
#define fi first
#define se second
#define pb push_back
#define ALL(a) (a).begin(), (a).end()
#define task "kbsiudthw"
#define LL long long
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef pair<int, ii> pii;
const int N = 1e5 + 5;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 2277;
vector<int> construct_permutation(long long k){
vi ans;
k--;
int sz = 0;
while (k){
FORD(i, 60, 1){
if (k < (1ll<<i) -1 ) continue;
k -= (1ll<<i) - 1;
sz = i;
break;
}
break;
}
int s = sz + __builtin_popcountll(k) - 1;
int cur = 0;
if (k & 1) ans.pb(cur++);
FOR (i, 1, sz){
ans.pb(s - i + 1);
if ((k>>i) & 1){
ans.pb(cur++);
}
}
reverse(ALL(ans));
return ans;
}
//int main(){
// vi a = construct_permutation(8);
// for(int &x : a) cout << x << ' ';
//}
