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// compile: make data
// run: time ./data < data.in
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) _debug_print(#x, x);
#define Debug(x...) _debug_print_format(#x, x);
#else
#define debug(x...)
#define Debug(x...)
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define VI vector<int>
#define VII vector<vector<int>>
#define VIII vector<vector<vector<int>>>
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0)
#define cmin(x,...) x=min({(x), __VA_ARGS__})
#define cmax(x,...) x=max({(x), __VA_ARGS__})
#define INTMAX (int)(9223372036854775807)
#define INF (int)(1152921504606846976)
#define double long double
#define int long long
#define MAXN 200010

struct graph {
    struct node {
        int u, v, w;
        int idx;
        bool operator<(const node &other) const {return w < other.w; }
        bool operator==(const node &other) const {return v == other.v && w == other.w; }
    };
    vector<vector<node>> e;
    vector<vector<int>> invid;
    node &inv(node &edge) {return e[edge.v][invid[edge.u][edge.idx]]; }

    int n;
    bool directed;
    graph(int V, bool D = 0) {
        n = V;
        e.resize(n), invid.resize(n);
        directed = D;
    }
    void add_edge(int u, int v, int w = 1, int wb = 1) {
        e[u].push_back(node{u, v, w, sz(e[u])});
        if (!directed) {
            e[v].push_back(node{v, u, wb, sz(e[v])});
            invid[u].push_back(sz(e[v]) - 1);
            invid[v].push_back(sz(e[u]) - 1);
        }
    }
    void graphviz_dump(string filename = "graph.dot") {
        ofstream gf; gf.open(filename);
        gf << (directed ? "digraph" : "graph") << " {\n";
        gf << "    "; rep(i, 0, n) gf << i << " ;"[i==n-1]; gf << endl;
        string notation = directed ? " -> " : " -- ";
        bool weighted = 0;
        for (auto es: e) for (auto edge: es) if (edge.w != 1) weighted = 1;
        rep(u, 0, n) {
            for (auto edge: e[u]) {
                int v = edge.v, w = edge.w;
                if (!directed && u > v) continue;
                gf << "    " << u << notation << v << (weighted ? " ;\n" : ";\n");
            }
        }
        gf << "}\n";
    }
    int eulerian_circuit(int s, vector<int> &route, int circuit = 1) {
        vector<int> din(n, 0), dout(n, 0);
        int E = 0;
        rep(u, 0, n) for (auto &edge: e[u]) {
            if (directed) ++din[edge.v], ++dout[u];
            else din[edge.v] += edge.v > u, dout[u] += edge.v > u;
            E += directed ? 1 : edge.v > u;
        }
        int error = 0;
        rep(i, 0, n) error += directed ? din[i] != dout[i] : (din[i] + dout[i]) & 1;
        if ((circuit && error) || (!circuit && error > 2)) return 0;
        vector<vector<int>> vis(n);
        rep(i, 0, n) vis[i].assign(sz(e[i]), 0);
        vector<int> cur(n, 0);
        function<void(int)> dfs = [&](int u) {
            for (; cur[u] < sz(e[u]); ++cur[u]) {
                int i = cur[u];
                int v = e[u][i].v;
                if (vis[u][i]) continue;
                vis[u][i] = 1;
                if (!directed) vis[v][inv(e[u][i]).idx] = 1;
                dfs(v);
            }
            route.push_back(u);
        };
        dfs(s);
        if (sz(route) != E+1) return 0;
        return 1;
    }
};

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);

    int n, m; cin >> n >> m;
    graph g(n);
    rep(i, 0, m) {
        int u, v; cin >> u >> v; --u, --v;
        g.add_edge(u, v);
    }
    g.graphviz_dump();
    vector<int> route; route.clear();
    int valid = g.undir_eulerian_circuit(0, route);
    if (!valid) cout << "IMPOSSIBLE" << endl;
    else rep(i, 0, sz(route)) cout << route[i]+1 << " \n"[i==sz(route)-1];

    return 0;
}
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Source: github.com/k4yt3x/flowerhd
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