#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"
namespace GETPATH {
VI vis;
VVPI gp;
VI order;
bool dfs(int u, int e) {
if (u == e) return true;
while (gp[u].size()) {
auto[v, i] = gp[u].back();
gp[u].pop_back();
if (vis[i]) continue;
vis[i] = true;
order.pb(i);
if (dfs(v, e)) return true;
order.pop_back();
}
return false;
}
};
int n, m;
VVPI gp;
VI getpath(int s, int e, VI exclude) {
GETPATH::vis = VI(m);
for (int x : exclude) GETPATH::vis[x] = true;
GETPATH::gp = gp;
GETPATH::order = VI();
if (GETPATH::dfs(s, e)) return GETPATH::order;
return {};
}
VI reverse(VI a) {
reverse(all(a));
return a;
}
int myus(int x) {
int type = !(x%2);
x = x/2*2 + type;
return x;
}
VI path;
VI ans;
void dfs(int u, int pi = -2) {
VI children;
for (auto[v, i] : gp[u]) if (i/2 != pi/2) children.pb(i);
if (children.size() >= 2) {
int a = children[0];
int b = children[1];
int ar = myus(a);
int br = myus(b);
for (int x : path) ans.pb(x);
ans.pb(a);
ans.pb(ar);
ans.pb(b);
ans.pb(br);
ans.pb(ar);
ans.pb(a);
ans.pb(br);
ans.pb(b);
for (int x : reverse(path)) ans.pb(x);
return;
} else {
for (auto[v, i] : gp[u]) if (i/2 != pi/2) {
path.pb(i);
dfs(v, i);
}
}
}
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});
if (N == 2) {
if (gp[0].size() < 2 || gp[1].size() < 1) return false;
VI ans;
ans.pb(gp[0][0].ss);
ans.pb(gp[1][0].ss);
ans.pb(gp[0][1].ss);
ans.pb(gp[0][0].ss);
ans.pb(gp[1][0].ss);
ans.pb(gp[0][1].ss);
return ans;
}
if (M == N*(N-1)) {
int a = gp[0][0].ss;
int b = gp[0][1].ss;
int ar = -1;
int br = -1;
for (auto[u, i] : gp[gp[0][0].ff]) if (u == b) ar = i;
for (auto[u, i] : gp[gp[0][1].ff]) if (u == a) br = i;
for (int x : path) ans.pb(x);
ans.pb(a);
ans.pb(ar);
ans.pb(b);
ans.pb(br);
ans.pb(ar);
ans.pb(a);
ans.pb(br);
ans.pb(b);
for (int x : reverse(path)) ans.pb(x);
}
/*rep(u, n) {*/
/* cout << "node " << u << endl;*/
/* for (auto[v, i] : gp[u]) cout << "via edge " << i << " to node " << v << endl;*/
/*}*/
dfs(0);
if (ans.size() == 0) return false;
return ans;
}
