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)

use std::cmp::min;
use std::collections::VecDeque;
use std::io::{stdin, Read};
use std::rc::Rc;
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let m = read::<usize>();
    let ab = (0..m)
        .map(|_| (read::<usize>(), read::<usize>()))
        .collect::<Vec<_>>();
    let mut edges = vec![vec![]; n + 1];
    for (a, b) in ab {
        edges[a].push(b)
    }

    let mut ans = vec![0; n + 1];
    let u_max = usize::max_value() as usize;

    for i in 1..n + 1 {
        let mut q = VecDeque::new();
        let mut dist = vec![u_max; n + 1];
        let mut prev = vec![0; n + 1];

        q.push_back((i, 0));

        while let Some((a, from)) = q.pop_front() {
            if from != 0 {
                if a == i {
                    if ans.len() > dist[from] + 1 {
                        let mut route = vec![];
                        let mut p = from;
                        while p != 0 {
                            route.push(p);
                            p = prev[p];
                        }
                        ans = route;
                    }
                } else {
                    if dist[a] == u_max {
                        prev[a] = from;
                        dist[a] = dist[from] + 1;
                        for &b in &edges[a] {
                            q.push_back((b, a));
                        }
                    }
                }
            } else {
                dist[a] = 0;
                for &b in &edges[a] {
                    q.push_back((b, a));
                }
            }
        }
    }

    let len = ans.len();
    if len <= n {
        println!("{}", len);
        for a in ans {
            println!("{}", a);
        }
    } else {
        println!("-1")
    }
}