#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int LOG = 64;
vector<int> construct_permutation(ll k) {
k--;
vector<int> perm;
vector<int> bits;
ll curr = 0;
for (int i = 0; i < LOG; i++) {
curr |= (1LL << i);
if (k >= curr) {
bits.push_back(i);
}
else break;
}
//curr /= 2;
//k -= curr;
if (k == curr/2) {
return bits;
}
vector<int> after;
bool flag = false;
for (int i = LOG-1; i >= 0; i--) {
if (!((k >> i) & 1)) continue;
if (!flag) {
flag = true;
}
else {
for (int j = 0; j < (int)bits.size(); j++) {
if (bits[j] >= i) bits[j]++;
}
bits.push_back(i);
}
}
for (auto &x: bits) x++;
bits.push_back(0);
return bits;
}
bool check(vector<int> a, ll x) {
x--;
int n = a.size();
vector<ll> dp(n, 0);
dp[0] = 1;
x--;
for (int i = 1; i < n; i++) {
dp[i] = 1;
for (int j = 0; j < i; j++) {
if (a[j] < a[i]) {
dp[i] += dp[j];
}
}
x -= dp[i];
}
if (x == 0) return true;
else return false;
}
