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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

type Graph = Vec<Vec<usize>>;

fn crcl(v:usize,org:usize,g:&Graph,mut used:&mut Vec<bool>,mut vs:&mut Vec<usize>){
    // eprintln!("{}",v);
    used[v] = true;
    for &to in &g[v] {
        if to==org {
            vs.push(v);
            return;
        }
        if used[to] {
            continue;
        }
        crcl(to,org,&g,&mut used,&mut vs);
        if !vs.is_empty() {
            vs.push(v);
            return;
        }
    }
}

fn main() {
    let (n,g) = {
        input!{
            n:usize,
            m:usize,
            ab:[(usize,usize);m]
        };
        let mut g = vec![Vec::new();n];
        for (a,b) in ab {
            g[a-1].push(b-1);
        }
        (n,g)
    };

    for i in 0..n {
        // eprintln!("# {}",i);
        let mut vs = Vec::new();
        let mut used = vec![false;n];
        crcl(i,i,&g,&mut used,&mut vs);
        if vs.len()>0 {
            vs = vs.into_iter().rev().collect();
            for _ in 0..n {
                let mut newvs:Vec<usize> = Vec::new();
                let mut flag = vec![None;n];
                for i in 0..vs.len() {
                    flag[vs[i]] = Some(i);
                }
                'outer: 
                for i in 0..vs.len() {
                    let v = vs[i];
                    for &to in &g[v] {
                        if let Some(id) = flag[to] {
                            if i!=vs.len()-1 && id<i || 0<id && id<i {
                                for i in id..(i+1) {
                                    newvs.push(vs[i]);
                                }
                                break 'outer;
                            }
                            if i+1<id {
                                for j in 0..(i+1){
                                    newvs.push(vs[j]);
                                }
                                for j in id..vs.len() {
                                    newvs.push(vs[j]);
                                }
                                break 'outer;
                            }
                        }
                    }
                }
                if !newvs.is_empty() {
                    vs = newvs;
                }
            }
            println!("{}",vs.len());
            let ans = vs.into_iter().map(|x|(x+1).to_string()).collect::<Vec<_>>().join("\n");
            println!("{}",ans);
            return;
        }
    }
    println!("-1");
}