#include <bits/stdc++.h>
using namespace std;
using vint = vector<int>;
using ll = long long;
using vll = vector<ll>;
using pint = pair<int, int>;
using vpint = vector<pint>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using pill = pair<int, ll>;
using vpill = vector<pill>;
using plli = pair<ll, int>;
using vplli = vector<plli>;
#define fi first
#define se second
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for(int i = (n)-1; i >= 0; --i)
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a)-1; i >= (b); --i)
vint construct_permutation(ll k)
{
bitset<64> b(k);
int LOG = __lg(k);
vint arr(LOG); iota(all(arr), 0);
int arr_max = LOG-1;
rrep(i, LOG) if (b[i]) {
if (i == 0) arr.insert(arr.begin(), ++arr_max);
else {
int pos = sz(arr)-i;
arr.insert(arr.begin(), arr[pos]);
FOR(j, pos+1, sz(arr)) arr[j]++;
arr_max++;
}
}
return arr;
}
