#include "islands.h"
#include <bits/stdc++.h>
#define pb push_back
#define f first
#define sc second
using namespace std;
typedef long long int ll;
typedef string str;
int n, m;
vector<int> U, V;
vector<vector<int>> initial_graph, initial_graph_r;
vector<bool> reachable;
vector<set<int>> in(n), out(n);
set<pair<int, int>> st;
void dfs_reachability(int nd){
if(reachable[nd]) return;
reachable[nd] = 1;
for(int x: initial_graph[nd]) dfs_reachability(x);
}
void remove_node(int nd){
st.erase({out[nd].size(), nd});
for(int i: in[nd]){
st.erase({out[U[i]].size(), U[i]});
out[U[i]].erase(i);
st.insert({out[U[i]].size(), U[i]});
}
for(int i: out[nd]) in[V[i]].erase(i);
out[nd].clear();
in[nd].clear();
}
void preprocess(){
in.resize(n);
out.resize(n);
for(int i = 0; i < m; i++){
if(!reachable[U[i]] || !reachable[V[i]]) continue;
out[U[i]].insert(i);
in[V[i]].insert(i);
}
for(int i = 0; i < n; i++){
st.insert({out[i].size(), i});
}
while(!st.empty() && st.begin()->f == 0) remove_node(st.begin()->sc);
}
vector<int> path_from_0(int nd){
vector<int> dis(n, -1);
queue<int> Q;
dis[0] = 0;
Q.push(0);
while(!Q.empty()){
int nd = Q.front(); Q.pop();
for(int x: initial_graph[nd]) if(dis[x] == -1){
dis[x] = dis[nd]+1;
Q.push(x);
}
}
vector<int> path;
while(nd != 0){
for(int i: initial_graph_r[nd]) if(dis[U[i]] == dis[nd]-1){
path.pb(i);
nd = U[i];
break;
}
}
reverse(path.begin(), path.end());
return path;
}
vector<bool> bl;
vector<int> cycle, to_cycle, cycle_nd;
bool found = 0;
void dfs(int nd, int i){
if(found) return;
if(bl[nd]){
while(cycle_nd.back() != nd){
cycle.pb(to_cycle.back());
to_cycle.pop_back();
cycle_nd.pop_back();
}
reverse(cycle.begin(), cycle.end());
cycle.pb(i);
found = 1;
return;
}
bl[nd] = 1;
to_cycle.pb(i);
cycle_nd.pb(nd);
for(int j: out[nd]) dfs(V[j], j);
if(!found){
to_cycle.pop_back();
cycle_nd.pop_back();
}
}
vector<int> path2;
vector<bool> cycle_bl;
void dfs2(int nd, int i){
if(found) return;
if(bl[nd]) return;
bl[nd] = 1;
path2.pb(i);
if(cycle_bl[nd]){
found = 1;
return;
}
for(int j: out[nd]) dfs2(V[j], j);
if(!found){
path2.pop_back();
}
}
variant<bool, vector<int>> find_journey(int _n, int _m, vector<int> _U, vector<int> _V){
n = _n, m = _m, U = _U, V = _V;
initial_graph.assign(n, {});
initial_graph_r.assign(n, {});
reachable.assign(n, 0);
for(int i = 0; i < m; i++) initial_graph[U[i]].pb(V[i]), initial_graph_r[V[i]].pb(i);
dfs_reachability(0);
preprocess();
set<int> cur = {0};
int ND = -1;
while(!cur.empty()){
for(int x: cur){
if(out[x].size() >= 2) ND = x;
}
if(ND != -1) break;
set<int> _cur;
for(int x: cur) for(int i: out[x]) _cur.insert(V[i]);
for(int x: cur) remove_node(x);
while(!st.empty() && st.begin()->f == 0) remove_node(st.begin()->sc);
swap(cur, _cur);
}
if(ND == -1) return false;
auto p1 = path_from_0(ND);
found = 0, cycle = {}, to_cycle = {}, cycle_nd = {ND};
bl.assign(n, 0);
bl[ND] = 1;
dfs(V[*out[ND].begin()], *out[ND].begin());
auto p2 = to_cycle, c1 = cycle;
cycle_bl.assign(n, 0);
for(int i: c1) cycle_bl[U[i]] = 1, cycle_bl[V[i]] = 1;
bl.assign(n, 0);
found = 0;
dfs2(V[*next(out[ND].begin())], *next(out[ND].begin()));
vector<int> ans;
if(found){
ans.insert(ans.end(), p1.begin(), p1.end());
ans.insert(ans.end(), p2.begin(), p2.end());
ans.insert(ans.end(), c1.begin(), c1.end());
ans.insert(ans.end(), p2.rbegin(), p2.rend());
ans.insert(ans.end(), path2.begin(), path2.end());
int k = -1;
for(int i = 0; i < c1.size(); i++) if(V[c1[i]] == V[path2.back()]) k = i;
for(int i = 0; i < c1.size(); i++) ans.pb(c1[int(int(k+c1.size())-i)%int(c1.size())]);
ans.insert(ans.end(), path2.rbegin(), path2.rend());
ans.insert(ans.end(), p1.rbegin(), p1.rend());
return ans;
}
found = 0, cycle = {}, to_cycle = {}, cycle_nd = {ND};
bl.assign(n, 0);
bl[ND] = 1;
dfs(V[*next(out[ND].begin())], *next(out[ND].begin()));
auto p3 = to_cycle, c2 = cycle;
ans.insert(ans.end(), p1.begin(), p1.end());
ans.insert(ans.end(), p2.begin(), p2.end());
ans.insert(ans.end(), c1.begin(), c1.end());
ans.insert(ans.end(), p2.rbegin(), p2.rend());
ans.insert(ans.end(), p3.begin(), p3.end());
ans.insert(ans.end(), c2.begin(), c2.end());
ans.insert(ans.end(), p3.rbegin(), p3.rend());
ans.insert(ans.end(), p2.begin(), p2.end());
ans.insert(ans.end(), c1.rbegin(), c1.rend());
ans.insert(ans.end(), p2.rbegin(), p2.rend());
ans.insert(ans.end(), p3.begin(), p3.end());
ans.insert(ans.end(), c2.rbegin(), c2.rend());
ans.insert(ans.end(), p3.rbegin(), p3.rend());
ans.insert(ans.end(), p1.rbegin(), p1.rend());
return ans;
}
