#include "islands.h"
#include <cassert>
#include <fstream>
#include <cstdio>
#include <variant>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <unordered_set>
#include <algorithm>
#include <iostream>
using namespace std;
variant<bool, vector<int>> find_journey(int N, int M, vector<int> U, vector<int> V) {
if (N == 2){
if(count(U.begin(), U.end(), 0) >= 2 && count(U.begin(), U.end(), 1) >= 1){
vector<pair<int, int>> ans(M);
for(int i = 0; i < M; i ++){
ans[i] = {U[i], i};
}
sort(ans.begin(), ans.end());
vector<int> ret = {ans[0].second, ans.back().second, ans[1].second, ans[0].second, ans.back().second, ans[1].second};
return ret;
}
return false;
}
bool N2 = true;
vector<int> counts(N);
for(int i = 0; i < M; i ++){
counts[U[i]]++;
counts[V[i]]++;
}
for(int i = 0; i < N; i ++){
N2 &= (counts[i] == 2 * N - 2);
}
if(N2 && N <= 1000){
vector<vector<pair<int, int>>> tree(N);
for(int i = 0; i < M; i ++){
tree[U[i]].push_back({V[i], i});
}
for(int i = 0; i < N; i ++){
sort(tree[i].begin(), tree[i].end());
}
vector<int> ret = {tree[0][0].second, tree[1][0].second, tree[0][1].second, tree[2][0].second, tree[1][0].second, tree[0][0].second, tree[2][0].second, tree[0][1].second};
return ret;
}
bool good = true;
for(int i = 0; i < M-1; i ++){
good = V[i] != V[i + 1];
}
if(good && N <= 1000){
vector<vector<pair<int,int>>> tree(N);
for(int i = 0; i < M; i ++){
tree[U[i]].push_back({V[i], i});
}
vector<int> path;
int id = 0, par = -1;
bool back = false;
int NNN = 0;
while(tree[id].size() < 3 && tree[id].size() > 0 && !back){
NNN = max(NNN, (int)tree[id].size());
if(tree[id].size() == 1){
par = id;
path.push_back(tree[id][0].second);
id = tree[id][0].first;
}
else{
if(tree[id][0].first == par){
path.push_back(tree[id][1].second);
par = id;
id = tree[id][1].first;
}
else{
path.push_back(tree[id][0].second);
par = id;
id = tree[id][0].first;
}
}
if(id == 0){
back = true;
}
}
if(!back && tree[0].size() != 0){
vector<int> mov, ids;
for(auto[l, r] : tree[id]){
if (l != par){
mov.push_back(l);
ids.push_back(r);
}
if(mov.size() > 1){
break;
}
}
for(int i = 0; i < M; i ++){
if(mov[0] == U[i] && id == V[i]){
ids.insert(ids.begin() + 1, i);
break;
}
}
for(int i = 0; i < M; i ++){
if(mov[1] == U[i] && id == V[i]){
ids.push_back(i);
break;
}
}
vector<int> gap;
if(mov[0] == mov[1]){
gap = {ids[0], ids[1], ids[2], ids[0], ids[1], ids[2]};
}
else{
gap = {ids[0], ids[1], ids[2], ids[3], ids[1], ids[0], ids[3], ids[2]};
}
vector<int> legit;
for(int i : path){
legit.push_back(i);
}
for(int i : gap){
legit.push_back(i);
}
reverse(path.begin(), path.end());
for(int i : path){
legit.push_back(i);
}
return legit;
}
return false;
}
vector<queue<int>> tree(N);
for(int i = 0; i < M; i ++){
tree[U[i]].push(V[i]);
}
vector<int> path, vis(N, 0);
path.push_back(0);
while(path.size()){
vis[path.back()] = true;
if(tree[path.back()].size()){
int a = tree[path.back()].front();
tree[path.back()].pop();
path.push_back(a);
if(vis[path.back()])break;
}
else{
vis[path.back()] = false;
path.pop_back();
}
}
if(path.size()){
return path;
}
return false;
}
