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)

use std::collections::VecDeque;
use std::collections::HashSet;

#[allow(unused_macros)]
macro_rules! input {
    ( $($t:ty),* ) => {{
        let mut s = String::new();
        std::io::stdin().read_line(&mut s);
        let mut splits = s.trim().split_whitespace();
        ($( { splits.next().unwrap().parse::<$t>().unwrap() },)*)
    }}
}



fn bfs(start: usize, to: &Vec<Vec<usize>>) -> Vec<usize> {

    let n = to.len();
    let mut will = VecDeque::new();
    let mut dist = vec![None; n];
    let mut from = vec![None; n];
    let mut last = None;

    dist[start] = Some(0);
    will.push_back(start);

    'outer: while let Some(now) = will.pop_front() {
        for next in &to[now] {
            if *next == start {
                last = Some((now, dist[now].unwrap()));
                break 'outer;
            }

            if dist[*next].is_some() {
                continue;
            }
            from[*next] = Some(now);
            dist[*next] = dist[now].map(|n| n + 1);
            will.push_back(*next);
        }
    }

    if let Some((l, min)) = last {
        let mut path = Vec::with_capacity(min);
        let mut v = l;
        path.push(v);
        while let Some(i) = from[v] {
            path.push(i);
            v = i;
        }
        return path;
    } else {
        return vec![];
    }
}

#[allow(unused_must_use)]
#[allow(unused_variables)]
fn solve() {
    let (n, m) = input!(usize, usize);

    let mut to = vec![vec![]; n];

    for i in 0..m {
        let (a, b) = input!(usize, usize);
        to[a - 1].push(b - 1);
    }

    let mut ans = vec![0; n];
    for i in 0..n {
        let mut went = HashSet::new();
        went.insert(i);

        let mut will = VecDeque::new();
        for next in &to[i] {
            will.push_back(*next);
        }

        let hs = bfs(i, &to);

        if hs.len() != 0 && hs.len() <= ans.len() {
            ans = hs;
        }
    }

    if ans.len() == n {
        println!("-1");
    } else {
        println!("{}", ans.len());
        for x in ans.iter() {
            println!("{}", x + 1);
        }
    }
}

fn main() {
    solve();
}