Problem:
Score : 600 points

Problem Statement

Given is a directed graph G with N vertices and M edges.

The vertices are numbered 1 to N, and the i-th edge is directed from Vertex A_i to Vertex B_i.

It is guaranteed that the graph contains no self-loops or multiple edges.

Determine whether there exists an induced subgraph (see Notes) of G such that the in-degree and out-degree of every vertex are both 1. If the answer is yes, show one such subgraph.

Here the null graph is not considered as a subgraph.

Notes

For a directed graph G = (V, E), we call a directed graph G' = (V', E') satisfying the following conditions an induced subgraph of G:

V' is a (non-empty) subset of V.

E' is the set of all the edges in E that have both endpoints in V'.

Constraints

1 \leq N \leq 1000

0 \leq M \leq 2000

1 \leq A_i,B_i \leq N

A_i \neq B_i

All pairs (A_i, B_i) are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

If there is no induced subgraph of G that satisfies the condition, print -1.
Otherwise, print an induced subgraph of G that satisfies the condition, in the following format:

K
v_1
v_2
:
v_K

This represents the induced subgraph of G with K vertices whose vertex set is \{v_1, v_2, \ldots, v_K\}. (The order of v_1, v_2, \ldots, v_K does not matter.)
If there are multiple subgraphs of G that satisfy the condition, printing any of them is accepted.

Sample Input 1

4 5
1 2
2 3
2 4
4 1
4 3

Sample Output 1

3
1
2
4

The induced subgraph of G whose vertex set is \{1, 2, 4\} has the edge set \{(1, 2), (2, 4), (4, 1)\}. The in-degree and out-degree of every vertex in this graph are both 1.

Sample Input 2

4 5
1 2
2 3
2 4
1 4
4 3

Sample Output 2

-1

There is no induced subgraph of G that satisfies the condition.

Sample Input 3

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2

Sample Output 3

4
2
3
4
5

Solution in C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

//{{{
#include<algorithm>
#include<cmath>
#include<deque>
#include<fstream>
#include<iomanip>
#include<iostream>
#include<map>
#include<numeric>
#include<queue>
#include<random>
#include<set>
#include<sstream>
#include<sys/time.h>
#include<unordered_map>
#include<unordered_set>
#include<vector>
using ll = long long;
enum : int { M = (int)1e9 + 7 };
enum : ll { MLL = (ll)1e18L + 9 };
using namespace std;
#ifdef LOCAL
#include"rprint2.hpp"
#else
#define FUNC(name) template <ostream& out = cout, class... T> void name(T&&...){ }
FUNC(printde) FUNC(printdbe) FUNC(printdwe) FUNC(printdu);
#endif
template <template <class T, class = std::allocator<T>> class V, class E>
istream& operator >> (istream& in, V<E>& v){ for(auto& e : v){ in >> e; } return in; }
//}}}

struct Graph{
    struct Node{
        vector<int> dests;
    };
    vector<Node> nodes;
    Graph(int num): nodes(num){ }
    int id(Node* n){ return n - &nodes[0]; }
    int id(Node& n){ return &n - &nodes[0]; }
    // void print(){ for(auto& node : nodes){ prints(id(node), node.dests); } }
    void add1Edge(int from, int dest){
        nodes[from].dests.push_back(dest);
    }
    void add2Edge2(int from, int dest){
        add1Edge(from, dest);
        add1Edge(dest, from);
    }
    bool dfs(int idx, unordered_set<int>& visited, vector<int>& vs, int from = -1){
        if(visited.count(idx)){
            int pos = 0;
            printde(visited, vs, idx);
            while(vs[pos] != idx){
                pos++;
            }
            int n2 = vs.size() - pos;
            for(int i = 0; i < pos; i++){
                vs[i] = vs[i + pos];
            }
            vs.resize(n2);
            return true;
        }
        vs.push_back(idx);
        visited.insert(idx);
        for(int didx : nodes[idx].dests){
            if(didx == from){ continue; }
            if(dfs(didx, visited, vs, idx)){
                printde(idx, vs);
                return true;
            }
        }
        vs.pop_back();
        visited.erase(idx);
        return false;
    }
};

int main(){
    cin.tie(0); ios::sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    Graph g(n);
    for(int i = 0; i < m; i++){
        int a, b;
        cin >> a >> b;
        a--; b--;
        g.add1Edge(a, b);
    }
    // g.print();
    unordered_set<int> visited;
    vector<int> vs;
    for(int i = 0; i < n; i++){
        vs.clear();
        visited.clear();
        g.dfs(i, visited, vs);
        printde(vs);
        if(vs.size()){
            break;
        }
    }
    printde(vs);
    if(vs.empty()){
        cout << -1 << '\n';
        return 0;
    }
    vs.push_back(vs[0]);
    while(1){
        unordered_map<int, int> vs2;
        for(size_t i = 0; i < vs.size() - 1; i++){
            vs2[vs[i]] = i;
        }
        for(size_t i = 0; i < vs.size() - 1; i++){
            auto& v = vs[i];
            for(auto& d : g.nodes[v].dests){
                if(d != vs[i + 1] && vs2.count(d)){
                    int i2 = vs2[d];
                    if(i2 > (int)i){
                        int cnt = 1;
                        while(i2 < (int)vs.size()){
                            vs[i + cnt] = vs[i2];
                            cnt++;
                            i2++;
                        }
                        vs.resize(i + cnt);
                    }else{
                        int n2 = i - i2 + 1;
                        for(int j = 0; j < n2; j++){
                            vs[j] = vs[i2 + j];
                        }
                        vs.resize(n2);
                        vs.push_back(vs[0]);
                    }
                    i = M;
                    goto cont;
                }
            }
        }
        break;
cont:
    printde(vs);
        ;
    }
    vs.pop_back();
    cout << vs.size() << '\n';
    for(auto& v : vs){
        cout << v + 1 << '\n';
    }
}