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 (1.15.1) (judge verdict: Wrong Answer)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (N, M): (usize, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    };
    let (A, B): (Vec<usize>, Vec<usize>) = {
        let (mut A, mut B) = (vec![], vec![]);
        for _ in 0..M {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            A.push(iter.next().unwrap().parse().unwrap());
            B.push(iter.next().unwrap().parse().unwrap());
        }
        (A, B)
    };
    let G = {
        let mut G = vec![std::collections::HashSet::new(); N + 1];
        for i in 0..M {
            G[A[i]].insert(B[i]);
        }
        G
    };

    const INF: usize = 1_000_000_000;
    fn f(
        i: usize,
        G: &Vec<std::collections::HashSet<usize>>,
        p: &mut Vec<usize>,
    ) -> (usize, usize) {
        // println!("{}", i);
        for &j in &G[i] {
            if p[j] != 0 && p[j] != INF {
                return (i, j);
            }
        }
        for &j in &G[i] {
            if p[j] == 0 {
                p[j] = i;
                let (l, r) = f(j, G, p);
                if l != INF {
                    return (l, r);
                }
            }
        }
        p[i] = INF;
        (INF, INF)
    }
    let mut p = vec![0; N + 1];
    let mut flag = true;
    for i in 1..(N + 1) {
        if p[i] == 0 {
            let (l, r) = f(i, &G, &mut p);
            if l != INF && flag {
                let mut j = l;
                let mut res = vec![];
                while j != r {
                    res.push(j);
                    j = p[j];
                }
                res.push(r);
                println!(
                    "{}\n{}",
                    res.len(),
                    res.iter()
                        .map(|r| r.to_string())
                        .collect::<Vec<_>>()
                        .join("\n")
                );
                flag = false;
            }
        }
    }
    if flag {
        println!("-1");
    }
}