#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<bool> vb;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,k,n) for(ll i=(ll)(k);i<(ll)(n);i++)
#define all(a) a.begin(),a.end()
#define fi first
#define se second
#define pb emplace_back
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<'\n';}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<'\n';}
const ll inf=1001001001001;
#include "islands.h"
std::variant<bool, std::vector<int>> find_journey(int N, int M, std::vector<int> U, std::vector<int> V) {
vvp g(N),rg(N);
rep(i,M){
g[U[i]].pb(V[i],i);
rg[V[i]].pb(U[i],i);
}
vi cnt(N);rep(i,N)cnt[i]=g[i].size();
vb dead(N,false);
queue<ll> que;
auto f=[&](ll i){
que.push(i);
while(!que.empty()){
ll t=que.front();que.pop();
for(auto x:rg[t])if(!dead[x.fi]){
cnt[x.fi]--;
if(cnt[x.fi]==0){
dead[x.fi]=true;que.push(x.fi);
}
}
}
};
auto loop=[&](ll s,vp v){
vi ver;
ver.pb(s);
for(auto x:v)ver.pb(x.fi);
ll i=0;
while(ver[i]!=ver.back())i++;
vi res;
rep(j,i)res.pb(v[j].se);
REP(j,i,v.size())res.pb(v[j].se);
for(ll j=i-1;j>=0;j--)res.pb(v[j].se);
return res;
};
auto rloop=[&](ll s,vp v){
vi ver;
ver.pb(s);
for(auto x:v)ver.pb(x.fi);
ll i=0;
while(ver[i]!=ver.back())i++;
vi res;
rep(j,i)res.pb(v[j].se);
for(ll j=v.size()-1;j>=i;j--)res.pb(v[j].se);
for(ll j=i-1;j>=0;j--)res.pb(v[j].se);
return res;
};
rep(i,N)if(!dead[i]&&cnt[i]==0){
dead[i]=true;f(i);
}
if(dead[0])return false;
ll cur=0;
vi ans;
while(true){
vp nex;
for(auto x:g[cur])if(!dead[x.fi])nex.pb(x);
if(nex.size()==0)return false;
if(nex.size()>1){
vb seen1(N,false),seen2(N,false);
vp a1,a2;
{
a1.pb(nex[0]);
seen1[cur]=true;
ll i=nex[0].fi;
while(!seen1[i]){
seen1[i]=true;
ll j=0;while(dead[g[i][j].fi])j++;
a1.pb(g[i][j]);
i=g[i][j].fi;
}
}
{
a2.pb(nex[1]);
seen2[cur]=true;
ll i=nex[1].fi;
while(!seen1[i]&&!seen2[i]){
seen2[i]=true;
ll j=0;while(dead[g[i][j].fi])j++;
a2.pb(g[i][j]);
i=g[i][j].fi;
}
if(!seen2[i]){
vi ver;
vp prev(N,P(-1,-1));
ver.pb(cur);
for(auto x:a1)ver.pb(x.fi);
ll l=0;
while(ver[l]!=ver.back())l++;
REP(i,l,ver.size()-1)prev[ver[i]]=P(ver[i+1],a1[i].se);
if(prev[a2.back().fi]!=P(-1,-1)){
rep(i,ver.size()-l-1){
a2.pb(prev[a2.back().fi]);
}
}
else{
ll idx=0;
while(a1[idx].fi!=a2.back().fi)idx++;
REP(i,idx+1,a1.size())a2.pb(a1[i]);
}
vi r1=loop(cur,a1),r2=rloop(cur,a2);
vector<int> res;
for(ll x:ans)res.pb(x);
for(ll x:r1)res.pb(x);
for(ll x:r2)res.pb(x);
reverse(all(ans));
for(ll x:ans)res.pb(x);
return res;
}
else{
vi r1=loop(cur,a1),r2=loop(cur,a2),r3=rloop(cur,a1),r4=rloop(cur,a2);
vector<int> res;
for(ll x:ans)res.pb(x);
for(ll x:r1)res.pb(x);
for(ll x:r2)res.pb(x);
for(ll x:r3)res.pb(x);
for(ll x:r4)res.pb(x);
reverse(all(ans));
for(ll x:ans)res.pb(x);
return res;
}
}
}
dead[cur]=true;f(cur);
cur=nex[0].fi;ans.pb(nex[0].se);
}
}
