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 (GCC 5.4.1) (judge verdict: Runtime Error)

//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize(3)
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC target("sse3","sse2","sse")
//#pragma GCC target("avx","sse4","sse4.1","sse4.2","ssse3")
//#pragma GCC target("f16c")
//#pragma GCC optimize("inline","fast-math","unroll-loops","no-stack-protector")
//#pragma GCC diagnostic error "-fwhole-program"
//#pragma GCC diagnostic error "-fcse-skip-blocks"
//#pragma GCC diagnostic error "-funsafe-loop-optimizations"
//#pragma GCC diagnostic error "-std=c++14"
#include "bits/stdc++.h"
//#include "ext/pb_ds/tree_policy.hpp"
//#include "ext/pb_ds/assoc_container.hpp"
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fr(x) freopen(x,"r",stdin)
#define fw(x) freopen(x,"w",stdout)
#define iout(x) printf("%d\n",x)
#define lout(x) printf("%lld\n",x)
#define REP(x,l,u) for(ll x = l;x<u;x++)
#define RREP(x,l,u) for(ll x = l;x>=u;x--)
#define complete_unique(a) a.erase(unique(a.begin(),a.end()),a.end())
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) begin(a),end(a)
#define PII pair<int,int>
#define PLL pair<ll,ll>
#define MP make_pair
#define lowbit(x) ((x)&(-(x)))
#define lson (ind<<1)
#define rson (ind<<1|1)
#define se second
#define fi first
#define sz(x) ((int)x.size())
#define EX0 exit(0);

typedef  long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
using namespace std;
typedef vector<ll> VLL;
typedef vector<int> VI;
const int block_size = 320;
typedef complex<ll> point;
const ll mod = 1e9+7;
const ll inf = 1e9+7;
const ld eps = 1e-9;
const db PI = atan(1)*4;
template<typename T>
inline int sign(const T&a) {if(a<0)return -1;if(a>0)return 1;return 0;}
string to_string(string s) {return '"' + s + '"';}string to_string(const char* s) {return to_string((string) s);}string to_string(bool b) {return (b ? "true" : "false");}template <typename A, typename B>string to_string(pair<A, B> p) {return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";}template <typename A>string to_string(A v) {bool first = true;string res = "{";for (const auto &x : v) {if (!first) {res += ", ";}first = false;res += to_string(x);}res += "}";return res;}void debug_out() { cerr << endl; }template <typename Head, typename... Tail>void debug_out(Head H, Tail... T) {cerr << " " << to_string(H);debug_out(T...);}

#ifndef ONLINE_JUDGE
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define dbg(...) {}
#endif

template<typename T,typename S>inline bool upmin(T&a,const S&b){return a>b?a=b,1:0;}
template<typename T,typename S>inline bool upmax(T&a,const S&b){return a<b?a=b,1:0;}

template<typename T> inline void in(T &x) {x = 0;T f = 1;char ch = getchar();while (!isdigit(ch)) {if (ch == '-') f = -1;ch = getchar();}while (isdigit(ch))  {x = x * 10 + ch - '0';ch = getchar();}x *= f;}
ll twop(int x) {return 1LL<<x;}
template<typename T>T MOD(T a, T m){a %= m;if (a < 0)a += m;return a;}
template<typename T>T inverse(T a, T m){a = MOD(a, m);if (a <= 1)return a;return MOD((1 - inverse(m, a) * m) / a, m);}template<typename A,typename B > inline void in(A&x,B&y) {in(x);in(y);}
template<typename A,typename B,typename C>inline void in(A&x,B&y,C&z) {in(x);in(y);in(z);}
template<typename A,typename B,typename C,typename D> inline void in(A&x,B&y,C&z,D&d) {in(x);in(y);in(z);in(d);}
template <typename T>T sqr(T x){return x*x;}
ll gcd(ll a,ll b){while(b!=0){a%=b;swap(a,b);}return abs(a);}
ll fast(ll a,ll b,ll mod){ll ans = 1;while(b){if(b&1){b--;ans = ans * a % mod;}else{a = a * a % mod;b/=2;}}return ans%mod;}



namespace SOLVE {
    int n,m;
    VI adj[10000];
    bool vis[10000];
    VI cycle;
    stack<int>s;
    bool ins[10000];
    void dfs(int cur){
        vis[cur] = 1;
        ins[cur] = 1;
        s.push(cur);
        if(sz(cycle))return;
        for(auto nxt:adj[cur]){
            if(ins[nxt]){
                
                while(s.top() != nxt){
                    cycle.PB(s.top());
                    s.pop();
                }
                cycle.PB(nxt);
                reverse(all(cycle));
                return;
            }else if(vis[nxt]){
                
            }else{
                dfs(nxt);
                if(sz(cycle))return;
            }
        }
        ins[cur] = 0;
        s.pop();
    }
    bool reduce(){
        VI id(n+1,-1);
//        dbg(cycle);
        REP(i,0,sz(cycle))id[cycle[i]] = i;
        REP(i,0,sz(cycle)){
            for(auto nxt:adj[cycle[i]]){
                if(id[nxt] == -1)continue;
                if(id[nxt] != (i+1)%sz(cycle)){
                    VI tmp(cycle.begin()+id[nxt],cycle.begin()+i+1);
//                    dbg(tmp);
                    swap(tmp,cycle);
                    
                    return true;
                }
            }
        }
        
        
        return false;
    }
    void main(){
        in(n,m);
        REP(i,0,m){
            int u,v;in(u,v);
            adj[u].PB(v);
        }
        REP(i,1,n+1){
            if(!vis[i]){
                dfs(i);
            }
        }
        if(!sz(cycle)){
            cout<<"-1";
        }else{
            while (reduce()) {
            }
            cout<<sz(cycle)<<endl;
            for(auto i:cycle)cout<<i<<endl;
        }













    }
}


signed main() {
    
    
    
    
    
    int t = 1;
//    in(t);
    for(int i = 1;i<=t;i++){
//        cout<<"Case #"<<i<<":";
        SOLVE::main();

    }
    
    
    
    
    
    
    
    
//    clock_t st = clock();
//    while(clock() - st < 3.0 * CLOCKS_PER_SEC){
//
//    }
    
    
    
    
    
    
    return 0;
}