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: Accepted)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn main() {
    use std::collections::VecDeque;
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let n: usize = scan(tokens);
    let mut d: Vec<Vec<usize>> = vec![Vec::new(); n];
    let m: usize = scan(tokens);
    for _ in 0..m {
        let a: usize = scan(tokens);
        let b: usize = scan(tokens);
        d[a - 1].push(b - 1);
    }
    let mut ans = Vec::new();
    let mut prev = vec![0; n];
    let mut visited = vec![false; n];
    let mut que = VecDeque::new();
    'a: for s in 0..n {
        for i in 0..n {
            visited[i] = false;
        }
        que.clear();
        que.push_back(s);
        while let Some(i) = que.pop_front() {
            for j in d[i].clone() {
                if j == s {
                    let mut res = Vec::new();
                    let mut k = i;
                    while {
                        res.push(k);
                        k != s
                    } {
                        k = prev[k];
                    }
                    res.reverse();
                    ans.push((res.len(), res));
                    continue 'a;
                }
                if !visited[j] {
                    visited[j] = true;
                    prev[j] = i;
                    que.push_back(j);
                }
            }
        }
    }
    if ans.is_empty() {
        println!("-1");
    } else {
        ans.sort();
        println!("{}", ans[0].0);
        for &k in &ans[0].1 {
            println!("{}", k + 1);
        }
    }
}