#include "islands.h"
#include <variant>
#include <vector>
#include <utility>
#include <functional>
#include <algorithm>
#include <iostream>
#include <set>
#include <queue>
using namespace std;
set<int> out[100005];
set<int> in[100005];
bool removed[100005];
bool visited[100005];
bool cycle[100005];
std::variant<bool, std::vector<int>> find_journey(
int N, int M, std::vector<int> U, std::vector<int> V) {
for (int i = 0; i < M; i++) {
out[U[i]].insert(i);
in[V[i]].insert(i);
}
queue<int> q;
for (int i = 0; i < N; i++) {
if (out[i].empty()) {
removed[i] = true;
q.push(i);
}
}
while (!q.empty()) {
int cur = q.front(); q.pop();
if (cur == 0) return false;
for (int k:in[cur]) {
out[U[k]].erase(k);
if (!removed[U[k]] && out[U[k]].empty()) {
removed[U[k]] = true;
q.push(U[k]);
}
}
in[cur].clear();
}
int st = 0;
vector<int> v;
while (1) {
if (out[st].size() >= 2) break;
else if (removed[st] || out[st].empty()) return false;
queue<int> q;
q.push(st);
removed[st] = true;
while (!q.empty()) {
int cur = q.front(); q.pop();
for (int k:in[cur]) {
if (removed[U[k]]) continue;
out[U[k]].erase(k);
if (out[U[k]].empty()) {
removed[U[k]] = true;
q.push(U[k]);
}
}
}
v.push_back(*out[st].begin());
st = V[v.back()];
}
for (int i = 0; i < N; i++) {
if (removed[i]) continue;
vector<int> to_remove;
auto it = ++out[i].begin();
if (i == st) ++it;
for (;it != out[i].end(); ++it) to_remove.push_back(*it);
for (int k:to_remove) out[i].erase(k);
}
visited[st] = true;
vector<int> t1;
t1.push_back(*out[st].begin());
int _end = -1;
while (1) {
int cur = V[t1.back()];
visited[cur] = true;
int nxt = *out[cur].begin();
t1.push_back(nxt);
if (visited[V[nxt]]) {
_end = V[nxt];
break;
}
else {
cur = V[nxt];
}
}
vector<int> str, cyc;
bool flag = false;
for (int i:t1) {
flag |= U[i] == _end;
if (flag) cyc.push_back(i);
else str.push_back(i);
}
for (int i:cyc) cycle[U[i]] = true;
fill(visited, visited + 100005, false);
vector<int> t2;
visited[st] = true;
t2.push_back(*++out[st].begin());
_end = -1;
while (1) {
int cur = V[t2.back()];
if (cycle[cur]) {
vector<int> ans;
for (int i:v) ans.push_back(i);
for (int i:str) ans.push_back(i);
for (int i:cyc) ans.push_back(i);
reverse(str.begin(), str.end());
for (int i:str) ans.push_back(i);
for (int i:t2) ans.push_back(i);
int pos = 0;
while (V[cyc[pos]] != cur) pos++;
for (int i = pos; i > pos - (int)cyc.size(); i--) {
ans.push_back(cyc[(i + (int)cyc.size()) % cyc.size()]);
}
reverse(t2.begin(), t2.end());
for (int i:t2) ans.push_back(i);
reverse(v.begin(), v.end());
for (int i:v) ans.push_back(i);
return ans;
}
visited[cur] = true;
int nxt = *out[cur].begin();
t2.push_back(nxt);
if (visited[V[nxt]]) {
_end = V[nxt];
break;
}
else {
cur = V[nxt];
}
}
vector<int> str2, cyc2;
flag = false;
for (int i:t2) {
flag |= U[i] == _end;
if (flag) cyc2.push_back(i);
else str2.push_back(i);
}
vector<int> ans;
for (int i:v) ans.push_back(i);
for (int i:str) ans.push_back(i);
for (int i:cyc) ans.push_back(i);
reverse(str.begin(), str.end());
for (int i:str) ans.push_back(i);
for (int i:str2) ans.push_back(i);
for (int i:cyc2) ans.push_back(i);
reverse(str2.begin(), str2.end());
for (int i:str2) ans.push_back(i);
reverse(str.begin(), str.end());
for (int i:str) ans.push_back(i);
reverse(cyc.begin(), cyc.end());
for (int i:cyc) ans.push_back(i);
reverse(str.begin(), str.end());
for (int i:str) ans.push_back(i);
reverse(str2.begin(), str2.end());
for (int i:str2) ans.push_back(i);
reverse(cyc2.begin(), cyc2.end());
for (int i:cyc2) ans.push_back(i);
reverse(str2.begin(), str2.end());
for (int i:str2) ans.push_back(i);
reverse(v.begin(), v.end());
for (int i:v) ans.push_back(i);
return ans;
}
