#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) {
return '"' + s + '"';
}
string to_string(const char* s) {
return to_string((string) s);
}
string to_string(bool b) {
return (b ? "true" : "false");
}
string to_string(vector<bool> v) {
bool first = true;
string res = "{";
for (int i = 0; i < static_cast<int>(v.size()); i++) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(v[i]);
}
res += "}";
return res;
}
template <size_t N>
string to_string(bitset<N> v) {
string res = "";
for (size_t i = 0; i < N; i++) {
res += static_cast<char>('0' + v[i]);
}
return res;
}
template <typename A>
string to_string(A v) {
bool first = true;
string res = "{";
for (const auto &x : v) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(x);
}
res += "}";
return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << to_string(H);
debug_out(T...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__);
struct edge {
int from;
int to;
edge(){};
edge(int _from, int _to) : from(_from), to(_to){};
};
variant<bool, vector<int>> find_journey(int n, int m, vector<int> A, vector<int> B) {
vector<edge> edges;
vector<set<int>> g(n);
vector<set<int>> rev_g(n);
auto rev = [&](int e) {
int u = edges[e].from, v = edges[e].to;
g[u].erase(e);
rev_g[v].erase(e);
};
auto add = [&](int e) {
int u = edges[e].from, v = edges[e].to;
g[u].insert(e);
rev_g[v].insert(e);
};
for (int i = 0; i < m; i++) {
edges.emplace_back(A[i], B[i]);
add(i);
}
int st = 0;
vector<int> trail;
set<pair<int, int>> pos;
for (int i = 0; i < n; i++) {
pos.insert(make_pair(g[i].size(), i));
}
while (true) {
bool change = false;
while (pos.size() && pos.begin()->first == 0) {
int v = pos.begin()->second;
pos.erase(pos.begin());
change = true;
vector<int> make;
for (int e : rev_g[v]) {
make.push_back(e);
}
for (int e : make) {
int u = edges[e].from;
pos.erase(make_pair(g[u].size(), u));
rev(e);
pos.insert(make_pair(g[u].size(), u));
}
}
while (g[st].size() < 2) {
if (g[st].empty()) {
return false;
}
vector<int> make;
for (int e : rev_g[st]) {
make.push_back(e);
}
for (int e : make) {
if (trail.size() && e == trail.back()) {
continue;
}
change = true;
int u = edges[e].from;
pos.erase(make_pair(g[u].size(), u));
rev(e);
pos.insert(make_pair(g[u].size(), u));
}
int e = *g[st].begin();
st = edges[e].to;
trail.push_back(e);
}
if (!change) {
break;
}
}
vector<int> path;
vector<int> cyc;
vector<bool> was(n);
vector<bool> in_queque(n);
vector<int> que;
vector<int> ed;
function<bool(int)> dfs = [&](int v) {
was[v] = true;
in_queque[v] = true;
que.push_back(v);
for (int e : g[v]) {
int u = edges[e].to;
if (in_queque[u]) {
bool done = false;
for (int es : ed) {
if (edges[es].from != u && !done) {
path.push_back(es);
} else {
cyc.push_back(es);
done = true;
}
}
cyc.push_back(e);
return true;
}
if (was[u]) {
continue;
}
ed.push_back(e);
if (dfs(u)) {
return true;
}
ed.pop_back();
}
in_queque[v] = false;
que.pop_back();
return false;
};
vector<int> path1, path2, cyc1, cyc2;
if (!dfs(st)) {
return false;
}
path1 = path;
cyc1 = cyc;
fill(in_queque.begin(), in_queque.end(), false);
fill(was.begin(), was.end(), false);
path.clear();
cyc.clear();
que.clear();
ed.clear();
for (int e : cyc1) {
rev(e);
swap(edges[e].from, edges[e].to);
add(e);
}
for (int e : cyc1) {
int v = edges[e].from;
vector<int> r;
if (v != st) {
for (int es : g[v]) {
if (es != e) {
r.push_back(es);
}
}
} else {
assert(path1.empty());
}
for (int es : r) {
rev(es);
}
}
if (path1.empty()) {
for (int e : cyc1) {
int v = edges[e].from;
if (v == st) {
for (int es : g[v]) {
if (es == e) {
continue;
}
int u = edges[es].to;
vector<int> make;
for (int E : g[v]) {
if (E != e) {
make.push_back(E);
}
}
for (int E : make) {
rev(E);
}
assert(dfs(u));
path2 = path;
cyc2 = cyc;
path2.insert(path2.begin(), es);
break;
}
assert(cyc2.size() && path2.size());
break;
}
}
} else {
int e = path1[0];
assert(edges[e].from == st);
rev(e);
assert(dfs(st));
path2 = path;
cyc2 = cyc;
}
vector<int> ret;
auto add_way = [&](vector<int> &a) {
for (int e : a) {
ret.push_back(e);
}
reverse(a.begin(), a.end());
};
bool same = false;
{
int sam = edges[cyc1[0]].from;
for (int e : cyc2) {
int v = edges[e].from;
if (v == sam) {
same = true;
}
}
}
add_way(trail);
for (int rot = 0; rot < (same ? 1 : 2); rot++) {
add_way(path1);
add_way(cyc1);
add_way(path1);
add_way(path2);
add_way(cyc2);
add_way(path2);
}
add_way(trail);
return ret;
}
