Graph Ordering

input/code.cpp: In instantiation of 'void fast_print(const std::vector<_Tp>&) [with T = int]':
input/code.cpp:244:12:   required from 'std::ostream& operator,(std::ostream&, const T&) [with T = std::vector<int>; std::ostream = std::basic_ostream<char>]'
input/code.cpp:612:8:   required from here
input/code.cpp:181:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for (int i = 1; i < v.size(); i++) {
input/code.cpp: In function 'void fast_scan(int&)':
input/code.cpp:133:31: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
 void fast_scan(int &x) { scanf("%d", &x); }
                          ~~~~~^~~~~~~~~~
input/code.cpp: In function 'void fast_scan(long long int&)':
input/code.cpp:134:37: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
 void fast_scan(long long &x) { scanf("%lld", &x); }...

/*
                                                                                                     
                                             `-:://:::-                                             
                                           `//:-------:/:`                                          
                                          .+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .o:--...```..---+/`                                        
                                       `/y+o/---....---:+o.                                         
                                   `...````-os+/:---:/+o/--.`                                       
              `-/+++++/:.      `...`       :h+d+oooo+/+-`   ...                                     
            `/++//:::://++-`....`         -.`//````````:`     `..`                                  
           `o+/::------://o/`           `-` -.          -`       `..`                               
 `---.-o/:./o/::-..``..-ЗАПУСКАЕМ      ..  ..            -`        `...       ``..``                
  `....o+:-++/:--.```..-://s.        `-`  .-              -`          `-o: .-//::::/:-`             
          `:s+/:--....-::/+s-`      .-   `-                -`           -///:--------:/:`           
           ./s+//:::::://oo-``..НЕЙРОННУЮ: СЕТЬ:::::::-`РАБОТЯГИ        `+:--........--:/`          
            .:ooo+++++osso-`    `.:-...`/` ./::-------:/:`   -`         :+--..``````.--:+:...-+:-`  
             `.-/+++++/+-.-`    -.   ``:so:/:--.......--:+`  `-```````o+/+--..`````..--:o/-..:s+:.  
                 ```````:``.. `-`     -` `+:--..`````..--/+-.../.`````..-o:--.......---/o.    `     
                        `:  `:-      -.  .o:--..`` ``..--:o`   `-`      `:o+:--------:+o-`          
                         `-`-...    ..   .o/--...```..--:+/`    `-`     `oy/so/////++o/.`           
                          -/`  `-` `- ``+s/o/:---...---:++.      `-`   .-../d://///:-.`             
                `.---..``-..-    .-/..`````-oo+/:::::/+o+-        `-``-`  `-.  ````                 
             `:++++/+++++-  ..``.-/:`      /y-:/++o++/:.`..`       ./.   `-                         
            -++/::::::://+/..:-``:` ..   `-.`  ```.```    `..`   `..`-` `-                          
       ``  -o//:--....-::/++` -.-`   `-`.-`                 `..`..`  `-.-                           
  -----ss+:++/:--.```..-://s.  /.     `::                    `-:.     ./`                           
  `````/:..+o/::-..``.--:/+s. ..-`   `-``-`                 ..` `-`  `-`-`                          
          `-s+/::-----::/+oo---``-` ..    .:-    ```      .-`     .-.-  `-`                         
           `:oo+//::://+os/..:`..-/:`      :y.-:::::::.`.-`        ./-`  `-`                        
            `./+oooooooo+/.`-    .-:...`.. .//:-------://`        `- `..` `:.                       
              ``.-::::-.``-/`  `-` `-  `oo:+:--.......--:/`      `-    `.:--h.``..```               
                          -.-`.-    .-   `+:--..`````..--//`    `-       /s-//::::::::.             
                         -` `/-      ..  .o:--..`` ``..--:o.```.-        `//:--------://`           
                        -` .-`.-`     -.`-o/--...```..--:+/.``-:....``:-.+:--....`...--:+`          
                       ..`-.   `-.   ``:os:o/:---...---:++.  `-     ``///+:-..``````.--:+-````-.`   
              `.:///////.-`      .:-..` -``-+o+/:::::/+o/.  `-         `:+:-..`````..--:o/:--/ys+-  
            `-++///////+o/. ``....`-.    :` `.:++++++/:.`  .-           -o/---......---/o.   `.`    
           `++//:-----::/+o:..`     .-`   :    ```````    .-           `+so+:--------:++-`          
  `````:-``:o/::-..`..--:/+o`         -.  `-             .-          `../../+o+////+o+:.`           
  -----syo/o+/:--.```..-://s.          .-` `-           .-        `...     ``-:////:-``             
       .` `/s//:--....-::/+s.            -. `-`        .-       `..`                                
           .+o+/:::--:://+s/-..`          .::+y  ```  .-     `..`                                   
            ./oo++////+oso-`   `....       :y-+:::::::/`   ...                                      
             `.:+oooooo/-`         `....-. .//:-------:/:-.`                                        
                ``...``                 /+:+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .+/--...```..--:+/`                                        
                                         `-o/:---...---:++.                                         
                                          `-+o+/:---:/+o/.                                          
                                            `.:+oooo+/-.`                                           
                                               ``````                                               
*/

#ifdef aimbot
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#endif

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <queue>
#include <ostream>
#include <istream>
#include <typeinfo>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <fstream>
#include <array>
#include <list>
#include <bitset>
#include <functional>
#include <random>
#include <cstring>
#include <chrono>

#define random escape__from__random__aetuhoetnuhshe
#define mt make_tuple
#define x first
#define y second
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define umap unordered_map
#define uset unordered_set
#define elif else if
#define len(v) ((int)v.size())
#define f(i, n) for (int i = 0; i < (n); i++)
#define rof(i, n) for (int i = ((n) - 1); i >= 0; i--) 
#define apply(v, act) for (auto &x : v) { act; }
#define log(args...) {string s = #args;deque<string> deq;\
string buf = "";int bal = 0;for (char c : s) {\
if (c == '(' || c == '[' || c == '{') {bal++;\
} else if (c == ')' || c == ']' || c == '}') {\
bal--;} else {if (bal == 0) {if (c == ',') {\
deq.pb(buf);buf = "";} else {if (c != ' ') {\
buf += c;}}}}}if (!buf.empty()) {deq.pb(buf);}\
smart_io::precall_print();smart_io::_print(deq, args);}

#define print    \
smart_io::precall_print(); \
cout,

#define scan cin,

#ifdef fast_allocator
const int MAXMEM = 200 * 1000 * 1024;
char _memory[MAXMEM];
size_t _ptr = 0;
void* operator new(size_t _x) { _ptr += _x; assert(_ptr < MAXMEM); return _memory + _ptr - _x; }
void operator delete (void*) noexcept {}
#endif

using namespace std;

char string_in_buffer[(int)260];


void fast_scan(int &x) { scanf("%d", &x); }
void fast_scan(long long &x) { scanf("%lld", &x); }
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
void fast_scan(double &x) { scanf("%lf", &x); }
void fast_scan(long double &x) { scanf("%Lf", &x); }
void fast_scan(char &x) { 
	scanf("%c", &x); 
	if (x == '\n') {
		fast_scan(x);
	}
}
void fast_scan(string &x) {
	scanf("%s", string_in_buffer);
	x = string(string_in_buffer);
}

template<class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
	fast_scan(p.first);
	fast_scan(p.second);
}

template <class T>
void fast_scan(vector<T> &v) {
	for (auto &x : v) fast_scan(x);
}

void fast_print(const int &x) { printf("%d", x); }
void fast_print(const unsigned int &x) { printf("%u", x); }
void fast_print(const long long &x) { printf("%lld", x); }
void fast_print(const unsigned long long &x) { printf("%llu", x); }
void fast_print(const double &x) { printf("%.15lf", x); }
void fast_print(const long double &x) { printf("%.15Lf", x); }
void fast_print(const char &x) { printf("%c", x); };
void fast_print(const string &x) { printf("%s", x.c_str());}
void fast_print(const char v[]) { fast_print((string)v); }

template<class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
	fast_print(p.first);
	fast_print(' ');
	fast_print(p.second);
}

template <class T>
void fast_print(const vector<T> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print(' ');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const vector<vector<T>> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print('\n');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const T &v) {
	for (const auto &x : v) {
		fast_print(x);
		fast_print(' ');
	}
}


using namespace std;


namespace smart_io {
	string print_start = "";
	string sep = " ";
	bool first_print = false;

	void precall_print() {
		fast_print(print_start);
		print_start = "\n";
		first_print = true;
	}

	void _print(deque<string>) {}
	template<class T, class... Args>
	void _print(deque<string> names, T elem, Args... args) {
		if (!first_print) {
			fast_print("\n");
		} else {
			first_print = false;
		}
		fast_print(names.front());
		fast_print(" = ");
		fast_print(elem);
		names.pop_front();
		_print(names, args...);
	}
} //namespace smart_io


template <class T>
ostream &operator,(ostream &os, const T &object) {
	if (!smart_io::first_print) {
		fast_print(smart_io::sep);
	} else {
		smart_io::first_print = false;
	}
	fast_print(object);
	return os;
}

template <class T>
istream &operator,(istream &is, T &object) {
	fast_scan(object);
	return is;
}

namespace random {
	using namespace std::chrono;
	mt19937 rng(duration_cast< milliseconds >(
		system_clock::now().time_since_epoch()
	).count());
	uniform_real_distribution<> prob_dist(0.0, 1.0);
};

namespace typedefs {
	typedef long long ll;
	typedef unsigned long long ull;
	typedef pair<int, int> pii;
	typedef long double ld;
}

namespace numbers_operation {
	template<class T>
	T floor_mod(T a, T b) {
		if (a >= 0 && b >= 0) return a % b;
		if (a <= 0 && b <= 0) return a % b;
		return abs(b) - (abs(a) % abs(b));
	}
}

using namespace numbers_operation;
using namespace typedefs;
using namespace random;

struct BipolarDisorder {
	int n;
	vector<vector<int>> g;
	vector<pii> edges;
	vector<int> uptime;
	vector<int> tin;
	vector<bool> used;
	vector<int> buff;
	vector<bool> pick;
	vector<int> order;

	vector<int> at;

	int timer = 0;

	void init_time(int v) {
		used[v] = true;
		at[timer] = v; 
		tin[v] = uptime[v] = timer++;
		for (int sub : g[v]) {
			if (used[sub]) continue;
			init_time(sub);
		}
	}

	void check(int v, int _forb) {
		used[v] = true;
		for (int sub : g[v]) {
			if (used[sub]) continue;
			if (sub == _forb) continue;
			check(sub, _forb);
		}
	}
	bool is_critical_slow(int v) {
		used = vector<bool>(n, false);
		int cnt = 0;
		for (int sub : g[v]) {
			if (used[sub]) continue;
			cnt++;
			check(sub, v);
		}
		return cnt >= 2;
	}
	vector<bool> crit;
	void go(int v, int _p) {
		used[v] = true;
		for (int sub : g[v]) {
			if (sub == _p) continue;
			if (used[sub]) {
				uptime[v] = min(uptime[v], tin[sub]);
			} else {
				go(sub, v);
				uptime[v] = min(uptime[v], uptime[sub]);
				if (uptime[sub] >= tin[v]) {
					crit[v] = true;
				}
			}
		}
	}

	void update_critical() {
		tin = vector<int>(n, 0);
		uptime = vector<int>(n, 0);
		used = vector<bool>(n, false);
		init_time(0);
		crit = vector<bool>(n, false);
		used = vector<bool>(n, false);
		go(0, -1);
		crit[0] = is_critical_slow(0);
	}

	int A = -1;

	struct Node {
		Node *l = NULL, *r = NULL, *pref = NULL;
		int prior;
		int size = 1;

		Node() {
			prior = rng();
		} 
	};

	int get_size(Node *node) {
		return node ? node->size : 0;
	}

	void update(Node *node) {
		node->size = get_size(node->l) + get_size(node->r) + 1;
	}

	Node *merge(Node *l, Node *r) {
		if (!l) return r;
		if (!r) return l;
		if (l->prior > r->prior) {
			l->r = merge(l->r, r);
			l->r->pref = l;
			update(l);
			return l;
		} else {
			r->l = merge(l, r->l);
			r->l->pref = r;
			update(r);
			return r;
		}
	}

	pair<Node*, Node*> split(Node *node, int k) {
		if (!node) return mp(node, node);
		if (get_size(node->l) >= k) {
			if (node->l) node->l->pref = NULL;
			auto t = split(node->l, k);
			node->l = NULL;
			update(node);
			return mp(t.x, merge(t.y, node));
		} else {
			if (node->r) node->r->pref = NULL;
			auto t = split(node->r, k - get_size(node->l) - 1);
			node->r = NULL;
			update(node);
			return mp(merge(node, t.x), t.y);
		}
	}

	int get_id(Node *node) {
		int id = get_size(node->l);
		while (node->pref) {
			if (node->pref->r == node) {
				id += 1 + get_size(node->pref->l);
			}
			node = node->pref;
		}
		return id;
	}

	Node *cart = NULL;

	vector<Node*> pres;

	void dfs(int v, int _p, int end) {
		buff.pb(v);
		if (v == end) {
			for (int x : buff) {
				pres[x] = new Node();
				cart = merge(cart, pres[x]);
				pick[x] = true;
			}
		}
		at[timer] = v;
		uptime[v] = tin[v] = timer++;
		used[v] = true;
		for (int sub : g[v]) {
			if (sub == _p) continue;
			if (used[sub]) {
				uptime[v] = min(uptime[v], tin[sub]);
			} else {
				dfs(sub, v, end);
				uptime[v] = min(uptime[v], uptime[sub]);
			}
		}
		buff.pop_back();
	}

	void echo(int v, int _p) {
		used[v] = true;

		if (!pick[v]) {
			buff.pb(v);
		}

		int B = at[uptime[v]];
		if (!buff.empty() && pick[B] && B != A) {
			int itA = get_id(pres[A]);
			int itB = get_id(pres[B]);
			if (itA < itB) {
				auto t = split(cart, itA + 1);
				for (int x : buff) {
					pres[x] = new Node();
					t.x = merge(t.x, pres[x]);
				}
				cart = merge(t.x, t.y);
			} else {
				reverse(buff.begin(), buff.end());
				auto t = split(cart, itB + 1);
				for (int x : buff) {
					pres[x] = new Node();	
					t.x = merge(t.x, pres[x]);
				}
				cart = merge(t.x, t.y);
			}
			for (int x : buff) {
				pick[x] = true;
			}
			buff.clear();
		}

		for (int sub : g[v]) {
			if (sub == _p) continue;
			if (used[sub]) continue;
			if (pick[v]) {
				A = v;
			}
			echo(sub, v);
		}
	}

	set<int> finded_crit;
	void _index(int v) {
		used[v] = true;
		for (int sub : g[v]) {
			if (used[sub]) continue;
			if (crit[sub]) {
				finded_crit.insert(sub);
			} else {
				_index(sub);
			}
		}
	}

	void init(int _n) {
		n = _n;
		g.resize(n);
		at.resize(2 * n);
		uptime.resize(n);
		tin.resize(n);
		timer = 0;
	}

	void add_edge(int a, int b) {
		g[a].pb(b);
		g[b].pb(a);
		edges.emplace_back(a, b);
	}

	vector<int> get_priors() {
		{
			used = vector<bool>(n, false);
			update_critical();
			used = vector<bool>(n, false);
			vector<int> pos;
			f(i, n) {
				if (crit[i]) continue;
				if (!used[i]) {
					if (len(g[i]) == 1) {
						pos.pb(i);
						used[i] = true;
					} else {
						finded_crit.clear();
						_index(i);
						if (len(finded_crit) <= 1) {
							pos.pb(i);
						}
					}
				}
			}
			if (len(pos) <= 1) {
				pos.pb(n - 1);
			}
			if (len(pos) != 2) {
				return {};
			}

			int start = pos[0];
			int end = pos[1];
			shuffle(pos.begin(), pos.end(), rng);

			used = vector<bool>(n, false);
			pick = vector<bool>(n, false);
			pres.resize(n, NULL);
			timer = 0;
			dfs(start, -1, end);
			buff.clear();
			used = vector<bool>(n, false);
			echo(start, -1);
			vector<int> p(n);
			f(i, n) {
				if (pres[i]) {
					p[i] = get_id(pres[i]);
				} else {
					return {};
				}
			}
			vector<int> in(n), out(n);
			for (pii edge : edges) {
				if (p[edge.x] > p[edge.y]) {
					swap(edge.x, edge.y);
				}
				in[edge.y]++;
				out[edge.x]++;
			}
			bool fail = false;
			f(i, n) {
				if (i != start && in[i] == 0) {
					fail = true;
				}
				if (i != end && out[i] == 0) {
					fail = true;
				}
			}
			if (!fail) {
				return p;
			} else {
				return {};
			}
		}
	}
};


signed main() {
	int n, m;
	scan n, m;
	BipolarDisorder dis;
	dis.init(n);
	f(i, m) {
		int a, b;
		scan a, b;
		a--;b--;
		dis.add_edge(a, b);
	}
	vector<int> p = dis.get_priors();
	if (p.empty()) {
		print "IMPOSSIBLE";
		return 0;
	}
	vector<int> order(n);
	f(i, n) {
		order[p[i]] = i;
	}
	apply(order, x++);
	print order;
}

Test 1

Group: 1, 4, 5

Verdict: ACCEPTED

Test 2

Group: 1, 5

Verdict: ACCEPTED

Test 3

Group: 1, 5

Verdict: ACCEPTED

Test 4

Group: 1, 5

Verdict: ACCEPTED

Test 5

Group: 1, 5

Verdict: ACCEPTED

Test 6

Group: 2, 3, 5

Verdict: ACCEPTED

Test 7

Group: 2, 3, 5

Verdict: ACCEPTED

Test 8

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 9

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 10

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 11

Group: 2, 3, 5

Verdict: ACCEPTED

Test 12

Group: 2, 3, 5

Verdict: ACCEPTED

Test 13

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 14

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 15

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 16

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 17

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 18

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 19

Group: 3, 4, 5

Verdict: ACCEPTED

Test 20

Group: 3, 4, 5

Verdict: ACCEPTED

Test 21

Group: 3, 4, 5

Verdict: ACCEPTED

Test 22

Group: 3, 4, 5

Verdict: ACCEPTED

Test 23

Group: 3, 5

Verdict: ACCEPTED

Test 24

Group: 3, 5

Verdict: ACCEPTED

Test 25

Group: 3, 5

Verdict: ACCEPTED

Test 26

Group: 3, 5

Verdict: ACCEPTED

Test 27

Group: 3, 5

Verdict: ACCEPTED

Test 28

Group: 5

Verdict: ACCEPTED

Test 29

Group: 5

Verdict: ACCEPTED

Test 30

Group: 4, 5

Verdict: ACCEPTED

Test 31

Group: 4, 5

Verdict: ACCEPTED

Test 32

Group: 4, 5

Verdict: ACCEPTED

Test 33

Group: 4, 5

Verdict: ACCEPTED

Test 34

Group: 5

Verdict: ACCEPTED

Test 35

Group: 5

Verdict: ACCEPTED

Test 36

Group: 5

Verdict: ACCEPTED

Test 37

Group: 1, 2, 3, 4, 5

Verdict: ACCEPTED

Test 38

Group: 2, 3, 5

Verdict: ACCEPTED

Test 39

Group: 2, 3, 5

Verdict: ACCEPTED

Test 40

Group: 2, 3, 5

Verdict: ACCEPTED

Test 41

Group: 1, 2, 3, 5

Verdict: ACCEPTED

Test 42

Group: 2, 3, 5

Verdict: ACCEPTED

Test 43

Group: 3, 4, 5

Verdict: ACCEPTED

Test 44

Group: 3, 4, 5

Verdict: ACCEPTED

Test 45

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 46

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 47

Group: 2, 3, 5

Verdict: ACCEPTED

Test 48

Group: 3, 4, 5

Verdict: ACCEPTED

Test 49

Group: 4, 5

Verdict: ACCEPTED