#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "islands.h"
int n, m;
VVPI gp;
stack<PII> st;
VI onstack, vis, visedge;
VI path, cycle;
int zerocycle = -1;
bool dfs(int u = 0, int pi = -1) {
/*cout << "currently at " << u << endl;*/
for (auto[v, i] : gp[u]) if (i != pi && !visedge[i]) {
/*cout << "trying to move to " << v << " via edge " << i << endl;*/
if (onstack[v]) {
/*cout << "CYCLE DETECTED" << endl;*/
cycle.pb(i);
while (st.size()) {
if (st.top().ff == v) break;
if (st.top().ff == 0) zerocycle = st.top().ss;
cycle.pb(st.top().ss);
st.pop();
}
while (st.size()) {
path.pb(st.top().ss);
st.pop();
}
reverse(all(path));
reverse(all(cycle));
/*for (int x : path) cout << x << " "; cout << "| ";*/
/*for (int x : cycle) cout << x << " "; cout << endl;*/
return true;
}
if (vis[v]) continue;
/*cout << "moved successfully" << endl;*/
vis[v] = true;
onstack[v] = true;
st.push({v, i});
visedge[i] = true;
if (dfs(v, i)) return true;
onstack[v] = false;
}
return false;
}
VI rev(VI a) {
reverse(all(a));
return a;
}
int myus(int x) {
int type = !(x%2);
return x/2*2+type;
}
variant<bool, VI> find_journey(int N, int M, VI U, VI V) {
n = N;
m = M;
gp = VVPI(n);
rep(i, m) gp[U[i]].pb({V[i], i});
onstack = vis = VI(n);
visedge = VI(m);
if (dfs());
else return false;
VI ans;
for (int x : path) ans.pb(x);
for (int x : cycle) ans.pb(x);
for (int x : rev(path)) ans.pb(x);
if (zerocycle) {
reverse(all(cycle));
int c = cycle.size();
int s = -1;
rep(i, c) {
cycle.pb(cycle[i]);
if (cycle[i] == zerocycle) s = i;
}
replr(i, s, s+c-1) ans.pb(cycle[i]);
} else {
path[0] = myus(path[0]);
for (int x : path) ans.pb(x);
for (int x : rev(cycle)) ans.pb(x);
for (int x : rev(path)) ans.pb(x);
}
return ans;
}
