#include "islands.h"
#include <variant>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;
vector <int> u,v,ke[200001],ke2[200001],adj[200001],boring,fun,res,ve;
int n,m,ch[200001],pos[200001],deg[200001];
pair <vector <int>, vector <int>> dfs(int s, int x){
vector <int> ve,cycle;
memset(pos,-1,sizeof(pos));
ve.push_back(x);
pos[x]=0;
x=u[x]^v[x]^s;
while (true){
int i=adj[x][0];
int y=u[i]^v[i]^x;
x=y;
if (pos[i]!=-1){
x=i;
break;
}
pos[i]=ve.size();
ve.push_back(i);
}
for (int i=pos[x];i<ve.size();i++)
cycle.push_back(ve[i]);
while (ve.size()>pos[x])
ve.pop_back();
return {ve,cycle};
}
bool check(vector <int> a, vector <int> b){
if (a.size()!=b.size())
return false;
memset(ch,0,sizeof(ch));
for (int i:a)
ch[i]=1;
int cnt=0;
for (int i:b)
cnt+=ch[i];
return (cnt==a.size());
}
vector <int> rev(vector <int> v){
reverse(v.begin(),v.end());
return v;
}
vector <int> operator +(vector <int> a, vector <int> b){
for (int i:b)
a.push_back(i);
return a;
}
variant <bool, vector <int>> find_journey(int N, int M, vector <int> U, vector <int> V) {
n=N,m=M,u=U,v=V;
for (int i=0;i<m;i++){
ke[u[i]].push_back(i);
ke2[v[i]].push_back(i);
deg[u[i]]++;
}
for (int i=0;i<n;i++)
if (!deg[i]){
ch[i]=1;
ve.push_back(i);
}
while (!ve.empty()){
int x=ve.back();
ve.pop_back();
ch[x]=1;
for (int i:ke2[x]){
int y=u[i]^v[i]^x;
if (!--deg[y])
ve.push_back(y);
}
}
if (ch[0])
return false;
int x=0;
while (deg[x]==1){
for (int i:ke[x]){
int y=u[i]^v[i]^x;
if (!ch[y]){
boring.push_back(i);
for (int i:ke2[x])
if (!--deg[u[i]^v[i]^x])
ve.push_back(u[i]^v[i]^x);
ch[x]=1;
x=y;
break;
}
}
}
if (!deg[x])
return false;
while (!ve.empty()){
int x=ve.back();
ve.pop_back();
ch[x]=1;
for (int i:ke2[x]){
int y=u[i]^v[i]^x;
if (!--deg[y])
ve.push_back(y);
}
}
if (ch[x])
return false;
for (int i=0;i<n;i++){
if (ch[i])
continue;
for (int j:ke[i])
if (!ch[u[j]^v[j]^i])
adj[i].push_back(j);
}
auto [ve,c]=dfs(x,adj[x][0]);
auto [ve2,c2]=dfs(x,adj[x][1]);
if (check(c,c2))
fun=ve+c+rev(ve)+ve2+rev(c2)+rev(ve2);
else
fun=ve+c+rev(ve)+ve2+c2+rev(ve2)+ve+rev(c)+rev(ve)+ve2+rev(c2)+rev(ve2);
return boring+fun+rev(boring);
}
