#include "perm.h"
#include <algorithm>
class intperm {
public:
std::vector<int> perm;
long long value;
intperm(std::vector<int> perm = {}, long long value = 1)
: perm(perm), value(value) {}
std::pair<int, int> get_bounds() {
return std::make_pair(*min_element(perm.begin(), perm.end()),
*max_element(perm.begin(), perm.end()));
}
friend bool operator<(const intperm &a, const intperm &b) {
return a.value < b.value;
}
friend intperm operator+(intperm a, intperm b) {
intperm nxt;
if (b < a) {
std::swap(a.perm, b.perm);
std::swap(a.value, b.value);
}
nxt.perm = b.perm;
int offs = (a.perm.empty() ? 0 : a.get_bounds().second + 1);
for (int &x : nxt.perm)
x += offs;
nxt.perm.insert(nxt.perm.end(), a.perm.begin(), a.perm.end());
nxt.value = a.value + b.value - 1;
return nxt;
}
friend intperm operator*(intperm a, intperm b) {
intperm nxt;
if (b < a) {
std::swap(a.perm, b.perm);
std::swap(a.value, b.value);
}
nxt.perm = b.perm;
int offs = (a.perm.empty() ? 0 : a.get_bounds().second + 1);
for (int &x : nxt.perm)
x += offs;
nxt.perm.insert(nxt.perm.begin(), a.perm.begin(), a.perm.end());
nxt.value = a.value * b.value;
return nxt;
}
};
const intperm ONE({}, 1);
const intperm TWO({0}, 2);
std::vector<int> construct_permutation(long long k) {
intperm ans;
int msb = 63 - __builtin_clzll(k);
for (long long i = msb - 1; i >= 0; i--) {
ans = ans * TWO;
if (k & (1ll << i)) {
ans = ans + TWO;
}
}
return ans.perm;
}
