#include "longesttrip.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
vi longest_trip(int n, int D)
{
random_start();
vi verts;
rep(i,n) verts.pb(i);
shuffle(all(verts),mt);
vi t1 = {verts[0]};
vi t2 = {verts[1]};
bool is_nc = 0;
rep2(i,2,n-1)
{
// forall(it,t1) cout << it << " ";
// cout << "t1\n";
// forall(it,t2) cout << it << " ";
// cout << "t2\n\n";
int v = verts[i];
if(los(0,1) == 0) swap(t1,t2);
if(are_connected({v},{t1.back()}))
{
t1.pb(v);
is_nc = 0;
}
else
{
if(is_nc)
{
is_nc = 1;
t2.pb(v);
}
else
{
if(are_connected({v},{t2.back()}))
{
is_nc = 1;
t2.pb(v);
}
else
{
for(int j = siz(t2)-1; j >= 0; j--)
{
t1.pb(t2[j]);
}
t2 = {v};
is_nc = 0;
}
}
}
}
vi ends1;
vi ends2;
if(siz(t1) == 1) ends1 = {t1[0]};
else ends1 = {t1[0],t1.back()};
if(siz(t2) == 1) ends2 = {t2[0]};
else ends2 = {t2[0],t2.back()};
if(!are_connected(t1,t2))
{
if(siz(t1) > siz(t2)) return t1;
return t2;
}
if(are_connected(ends1,ends2))
{
if(are_connected(ends1,{ends2[0]}))
{
if(are_connected({ends1[0]},{ends2[0]}))
{
reverse(all(t1));
forall(it,t2) t1.pb(it);
return t1;
}
else
{
forall(it,t2) t1.pb(it);
return t1;
}
}
else
{
reverse(all(t2));
if(are_connected({ends1[0]},{ends2.back()}))
{
reverse(all(t1));
forall(it,t2) t1.pb(it);
return t1;
}
else
{
forall(it,t2) t1.pb(it);
return t1;
}
}
}
int l = 0;
int r = siz(t1)-2;
int ans = t1[siz(t1)-1];
while(l <= r)
{
int mid = (l+r)/2;
vi new_t1;
rep(i,mid+1) new_t1.pb(t1[i]);
if(are_connected(new_t1,t2))
{
ans = t1[mid];
r = mid-1;
}
else
{
l = mid+1;
}
}
l = 0;
r = siz(t2)-2;
int ans2 = t2[siz(t2)-1];
while(l <= r)
{
int mid = (l+r)/2;
vi new_t2;
rep(i,mid+1) new_t2.pb(t2[i]);
if(are_connected({ans},new_t2))
{
ans2 = t2[mid];
r = mid-1;
}
else
{
l = mid+1;
}
}
vi nt1;
int p1 = 0;
rep(i,siz(t1))
{
if(t1[i] == ans) p1 = i;
}
rep(i,siz(t1))
{
nt1.pb(t1[p1]);
p1++;
p1 %= siz(t1);
}
reverse(all(nt1));
int p2 = 0;
rep(i,siz(t2))
{
if(t2[i] == ans2) p2 = i;
}
rep(i,siz(t2))
{
nt1.pb(t2[p2]);
p2++;
p2 %= siz(t2);
}
return nt1;
}
