#include "islands.h"
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#define dbg(...) printf(__VA_ARGS__);
#define getchar_unlocked getchar
#else
#define dbg(...)
#endif
#define sf scanf
#define pf printf
#define fi first
#define se second
#define pb push_back
#define psf push_front
#define ppb pop_back
#define ppf pop_front
#define sz(x) (int)x.size()
#define mnto(x,y) x=min(x,(__typeof__(x))y)
#define mxto(x,y) x=max(x,(__typeof__(x))y)
#define INF 1023456789
#define LINF 1023456789123456789
#define all(x) x.begin(),x.end()
#define lb(x,v) (lower_bound(all(x),v)-x.begin())
#define ub(x,v) (upper_bound(all(x),v)-x.begin())
#define disc(x) sort(all(x));x.resize(unique(all(x))-x.begin());
typedef long long ll;
typedef long double ld;
typedef pair<int,int> ii;
typedef pair<ll,ll> pll;
typedef tuple<int,int,int> iii;
typedef tuple<int,int,int,int> iiii;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
mt19937 rng(time(0));
#define maxn 200005
int mxdep[maxn],pedge[maxn],par[maxn],dep[maxn];
bool vis[maxn],onstk[maxn],down[maxn],incycle[maxn],bothcycle[maxn];
map<int,ii> edgeid[maxn];
vi ans,cyclenode[2],tocycle[2],tocycleid[2],cycleid[2];;
vii AL[maxn];
void add(vector<int> &v){
for(int x:v)ans.pb(x);
}
void addrev(vector<int> &v){
for(int i=sz(v)-1;i>=0;--i)ans.pb(v[i]);
}
void dfs(int u){
vis[u]=onstk[u]=true;
mxdep[u]=-1;
for(auto[v,i]:AL[u]){
if(!vis[v]){
pedge[v]=i;
par[v]=u;
dep[v]=dep[u]+1;
dfs(v);
down[i]=true;
}
if(onstk[v])mxto(mxdep[u],dep[v]);
else{
mxto(mxdep[u],mxdep[v]);
down[i]=true;
}
}
onstk[u]=false;
}
bool getcyc(int u,vi &nodes){
vis[u]=onstk[u]=true;
for(auto[v,i]:AL[u]){
if(!vis[v]){
if(getcyc(v,nodes)){
nodes.pb(u);
return true;
}
}
if(onstk[v]){
nodes.pb(v),nodes.pb(u);
return true;
}
}
onstk[u]=false;
return false;
}
variant<bool,vi> find_journey(int N,int M,vi U,vi V){
for(int i=0;i<M;++i){
AL[U[i]].pb({V[i],i});
if(edgeid[U[i]].find(V[i])==edgeid[U[i]].end())edgeid[U[i]][V[i]]={i,i};
else edgeid[U[i]][V[i]].se=i;
}
dfs(0);
for(int rt=0;rt<N;++rt){
vi goodedge;
for(auto[x,i]:AL[rt]){
if(down[i]&&mxdep[x]>=dep[rt])goodedge.pb(x);
}
if(sz(goodedge)<2)continue;
vi pathtort;
int tmp=rt;
while(tmp){
pathtort.pb(pedge[tmp]);
tmp=U[pedge[tmp]];
}
reverse(all(pathtort));
add(pathtort);
for(int i=0;i<2;++i){
int x=goodedge[i];
memset(vis,false,sizeof vis);
memset(onstk,false,sizeof onstk);
for(int x:pathtort)vis[U[x]]=vis[V[x]]=true;
vis[rt]=onstk[rt]=true;
vi nodes;
getcyc(x,nodes);
nodes.pb(rt);
while(true){
tocycle[i].pb(nodes.back());
if(nodes.back()!=nodes[0])nodes.ppb();
else break;
}
reverse(all(nodes));
swap(nodes,cyclenode[i]);
}
int type=0;
for(int i:cyclenode[0])incycle[i]=true;
for(int i:cyclenode[1]){
if(incycle[i]){
bothcycle[i]=true;
if(i!=rt)type=1;
}
}
for(int x=0;x<2;++x){
for(int i=0;i<sz(tocycle[x])-1;++i){
int u=tocycle[x][i],v=tocycle[x][i+1];
tocycleid[x].pb(edgeid[u][v].fi);
swap(edgeid[u][v].fi,edgeid[u][v].se);
}
for(int i=0;i<sz(cyclenode[x])-1;++i){
int u=cyclenode[x][i],v=cyclenode[x][i+1];
cycleid[x].pb(edgeid[u][v].fi);
swap(edgeid[u][v].fi,edgeid[u][v].se);
}
}
if(type==0){//disjoint cycle
for(int x=0;x<2;++x){
add(tocycleid[x]);
add(cycleid[x]);
addrev(tocycleid[x]);
}
for(int x=0;x<2;++x){
add(tocycleid[x]);
addrev(cycleid[x]);
addrev(tocycleid[x]);
}
}
else{//overlapping cycle
add(tocycleid[0]);
add(cycleid[0]);
addrev(tocycleid[0]);
add(tocycleid[1]);
vi added;
for(int i:cycleid[1]){
int u=U[i],v=V[i];
if(u!=rt&&bothcycle[u]){
int start=-1;
for(int j=0;j<sz(cycleid[0]);++j){
int id=cycleid[0][j];
int u2=U[id],v2=V[id];
if(v2==u)start=j;
}
for(int j=start;j>=0;--j)ans.pb(cycleid[0][j]);
for(int j=sz(cycleid[0])-1;j>start;--j)ans.pb(cycleid[0][j]);
break;
}
ans.pb(i);
added.pb(i);
}
addrev(added);
addrev(tocycleid[1]);
}
addrev(pathtort);
return ans;
}
return false;
}
