#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<vi>;
using vvi = V<vi>;
#include "longesttrip.h"
std::vector<int> longest_trip(int N, int D)
{
if (D == 3) {
vi A(N);
iota(all(A), 0);
return A;
}
if (D == 2) {
vi A;
A.pb(0);
set<int> res;
fnr(i, 1, N) res.insert(i);
while (res.size() >= 2) {
int x = *res.begin(), y = *next(res.begin());
A.pb(are_connected({A.back()}, {x}) ? x : y);
res.erase(A.back());
}
int x = *res.begin();
if (are_connected({ A.back() }, {x})) A.pb(x);
else {
reverse(all(A));
A.pb(x);
}
return A;
}
vi idx(N);
iota(all(idx), 0);
srand(time(0));
random_shuffle(all(idx));
vi A{idx[0]}, B{idx[1]};
fnr(j, 2, N) {
int i = idx[j];
if (are_connected({i}, {A.back()})) {
A.pb(i);
} else if (are_connected({i}, {B.back()})) {
B.pb(i);
} else {
A.insert(A.end(), B.rbegin(), B.rend());
B = {i};
}
}
if (A.size() < B.size()) swap(A, B);
if (!are_connected(A, B)) return A;
if (B.size() == 1) {
A.pb(B[0]);
return A;
}
if (are_connected({A[0], A.back()}, {B[0], B.back()})) {
if (are_connected({A.back()}, {B[0]})) A.insert(A.end(), all(B));
else if (are_connected({A.back()}, {B.back()})) A.insert(A.end(), B.rbegin(), B.rend());
else if (are_connected({A[0]}, {B.back()})) B.insert(B.end(), all(A)), A = B;
else {
reverse(all(A));
A.insert(A.end(), all(B));
}
return A;
}
return A;
int l = 0, r = A.size()-1;
while (l != r) {
int m = (l+r)/2;
if (are_connected(vi(A.begin()+l, A.begin()+m+1), B)) r = m;
else l = m+1;
}
int ax = l;
l = 0, r = B.size()-1;
while (l != r) {
int m = (l+r)/2;
if (are_connected({A[ax]}, vi(B.begin()+l, B.begin()+m+1))) r = m;
else l = m+1;
}
int bx = l;
rotate(A.begin(), A.begin()+ax, A.end());
rotate(B.begin(), B.begin()+bx, B.end());
reverse(all(A));
A.insert(A.end(), all(B));
return A;
}
