#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
void add(vector < int > &v, int pos, int x){
vector < int > nw;
for(ll i = 0; i < pos; i++) nw.push_back(v[i]);
nw.push_back(x);
for(ll i = pos; i < v.size(); i++) nw.push_back(v[i]);
v = nw;
}
vector < ll > calc(vector < int > &v) {
vector < ll > dp(v.size() + 1, 0);
dp[0] = 1;
for(int x : v)
for(int i = 0; i <= x; i++)
dp[x + 1] += dp[i];
return dp;
}
vector < int > construct_permutation(ll k){
ll x = 0, s = 0, y = 1;
vector < int > ans;
vector < int > fac = {3, 2};
while(1){
ll f = fac[s];
y *= f, s = (s + 1) % fac.size();
if(y > k) break;
if(f == 3){
for(ll i = f - 2; i >= 0; i--) ans.push_back(x + i);
x += f - 1;
}
}
while(1){
ll sum = 0, pos = 1;
vector < ll > dp = calc(ans);
for(ll val : dp) sum += val;
if(sum == k) break;
for(ll i = 0; i < dp.size(); i++){
if(sum + dp[i] <= k){
pos = i;
sum += dp[i];
}
}
add(ans, pos, x++);
}
return ans;
}
