#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <unordered_map>
#include <unordered_set>
#define ll int
#define ld long double
#define pl pair<ll, ll>
#define vi vector<ll>
#define vii vector<vi>
#define vc vector<char>
#define vcc vector<vc>
#define vp vector<pl>
#define mi map<ll,ll>
#define mc map<char,int>
#define sortx(X) sort(X.begin(),X.end());
#define all(X) X.begin(),X.end()
#define allr(X) X.rbegin(),X.rend()
#define ln '\n'
#define YES {cout << "Alice\n"; return;}
#define NO {cout << "Bob\n"; return;}
#define MUN {cout << "-1\n"; return;}
const int MODE = 1e9 + 7;
using namespace std;
/*
eulerian circuit: that path start and end at the same vertex and visits every edge exactly once.
eulerian path: that path may start and end at different vertices and visits every edge exactly once.
in an undirected graph:
- an eulerian circuit exists if and only if every vertex has even degree and the graph is connected.
- an eulerian path if it's eulerian circuit or if it has exactly two vertices with odd degree and the graph is connected.
in directed graph:
- an eulerian circuit exists if and only if every vertex has equal in-degree and out-degree and the graph is strongly connected.
- an eulerian path exists if it has exactly one vertex with (out-degree - in-degree) = 1, exactly one vertex with (in-degree - out-degree) = 1, and all other vertices have equal indegree and out-degree.
*/
class Graph {
public:
int size;
vp Edge;
vii adj;
bool isConnected()
{
ll summ = 0, n = 0, src = -1;
vi visited(size + 1);
stack<int> stack;
for (int i = 0; i < adj.size(); i++)
if (!adj[i].empty()) n++, src = i;
if (src != -1) stack.push(src);
while (!stack.empty())
{
int m = stack.top();
stack.pop();
if (visited[m]) continue;
visited[m] = 1, summ++;
for (auto a : adj[m])
if (!visited[a]) stack.push(a);
}
return (summ == n);
}
/* The function returns one of the following values
0 --> If graph is not Eulerian
1 --> If graph has an Euler path (Semi-Eulerian)
2 --> If graph has an Euler Circuit (Eulerian) */
int isEulerian()
{
if (!isConnected()) return 0;
int odd = 0;
for (int i = 0; i <= size; i++)
odd += (adj[i].size() & 1);
if (odd > 2) return 0;
return (odd)? 1 : 2;
}
vii EulerPath(ll src) {
vii X;
stack<ll> st;
st.push(src);
vector<deque<pl>> Y(size + 1);
vi visted(Edge.size());
for (int i = 0; i < Edge.size(); i++)
{
int u = Edge[i].first, v = Edge[i].second;
Y[u].push_back({v, i});
Y[v].push_back({u, i});
}
stack<ll> tm;
vi ontm(size + 10);
while (!st.empty())
{
ll m = st.top();
bool isit = 1;
while (!Y[m].empty()) {
pl at = Y[m].front();
Y[m].pop_front();
if (visted[at.second]) continue;
visted[at.second] = 1;
st.push(at.first);
isit = 0;
break;
}
if (isit) {
if (ontm[m]) {
vi Y;
while (ontm[m]) {
ll tp = tm.top();
ontm[tp] = 0;
Y.push_back(tp);
tm.pop();
}
X.push_back(Y);
}
tm.push(m);
ontm[m] = 1;
st.pop();
}
}
reverse(all(X));
return (X);
}
void addEdge(int u, int v) {
adj[u].push_back(v);
adj[v].push_back(u);
Edge.push_back({u, v});
}
Graph(ll n) {
size = n;
adj.resize(n + 1);
}
};
void solve(int tc) {
ll n, m;
cin >> n >> m;
Graph gr(n+1);
for (int i = 0; i < m; i++)
{
ll u, v; cin >> u >> v;
gr.addEdge(u, v);
}
auto res = gr.EulerPath(1);
for (auto Z : res) {
for (auto a : Z) cout << a << ' ';
cout << '\n';
}
}
int main()
{
ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
int size = 1;
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
// cin >> size;
for (int i = 1; i <= size; i++)
solve(i);
}
