#include <bits/stdc++.h>
using namespace std;
#define MASK(x) (1LL << (x))
#define BIT(x, i) (((x) >> (i)) & 1)
#define ALL(x) (x).begin(), (x).end()
#define REP(i, n) for (int i = 0, _n = n; i < _n; ++i)
#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 FORE(it, s) for (__typeof(s.begin()) it = (s).begin(); it != (s).end(); ++it)
template <class U, class V> bool maximize(U &A, const V &B) { return (A < B) ? (A = B, true) : false; }
template <class U, class V> bool minimize(U &A, const V &B) { return (A > B) ? (A = B, true) : false; }
vector <int> construct_permutation(long long K) {
vector <int> bit;
for (; K > 0; K /= 2) {
bit.push_back(K % 2);
}
bit.pop_back(); reverse(ALL(bit));
vector <int> ans;
int cur = 0;
for (auto x : bit) {
ans.push_back(cur++);
if(x == 1) ans.insert(ans.begin(), cur++);
}
return ans;
}
