#include "islands.h"
#include <bits/stdc++.h>
using namespace std;
const int maxN = 1e5 + 20;
vector<pair<int, int>> adj1[maxN];
vector<pair<int, int>> adj2[maxN];
pair<int, int> nxt[maxN];
pair<int, int> prv[maxN];
int deg[maxN];
bool rem[maxN];
variant<bool, vector<int>> find_journey(int N, int M, vector<int> U, vector<int> V) {
for (int i = 0; i < M; i++) {
adj1[U[i]].emplace_back(V[i], i);
adj2[V[i]].emplace_back(U[i], i);
deg[U[i]]++;
}
deque<int> Q;
for (int i = 0; i < N; i++) {
if (deg[i] == 0) {
rem[i] = true;
Q.push_back(i);
}
}
vector<int> res;
int start = 0;
pair<int, int> nxt1, nxt2;
while (true) {
while (!Q.empty()) {
int u = Q.front();
Q.pop_front();
for (auto e: adj2[u]) {
int v = e.first;
if (rem[v]) {
continue;
}
deg[v]--;
if (deg[v] == 0) {
rem[v] = true;
Q.push_back(v);
}
}
}
if (rem[start]) {
return false;
}
nxt1 = {-1, -1};
nxt2 = {-1, -1};
for (auto e: adj1[start]) {
if (!rem[e.first]) {
if (nxt1.first == -1) {
nxt1 = e;
}
else if (nxt2.first == -1) {
nxt2 = e;
}
}
}
if (nxt1.first == -1) {
return false;
}
if (nxt2.first == -1) {
rem[start] = true;
Q.push_back(start);
start = nxt1.first;
res.push_back(nxt1.second);
}
else {
break;
}
}
for (int i = 0; i < N; i++) {
if (rem[i] || i == start) {
continue;
}
for (auto e: adj1[i]) {
if (!rem[e.first]) {
nxt[i] = e;
break;
}
}
}
bool skip = false;
int extra = -1;
for (int iter = -1; iter < 4; iter++) {
for (int i = 0; i < N; i++) {
prv[i] = {-1, -1};
}
if (skip) {
start = nxt2.first;
extra = nxt2.second;
}
else {
nxt[start] = (iter == -1 ? nxt2 : ((iter & 1) ? nxt2 : nxt1));
}
int u = start;
prv[start] = {start, -1};
while (true) {
int v = nxt[u].first;
if (prv[v].first != -1) {
if (iter == -1) {
if (v == start) {
swap(nxt1, nxt2);
}
break;
}
skip = (iter == 0 && v == start);
nxt[v] = {u, nxt[u].second};
vector<int> cycle = {nxt[u].second};
while (u != v) {
cycle.push_back(prv[u].second);
nxt[u] = prv[u];
u = prv[u].first;
}
vector<int> suf;
while (u != start) {
suf.push_back(prv[u].second);
u = prv[u].first;
}
if (extra != -1) {
suf.push_back(extra);
}
res.insert(res.end(), suf.rbegin(), suf.rend());
res.insert(res.end(), cycle.rbegin(), cycle.rend());
res.insert(res.end(), suf.begin(), suf.end());
break;
}
else {
prv[v] = {u, nxt[u].second};
u = v;
}
}
if (extra != -1) {
break;
}
}
return res;
}
