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(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

fn solve() {
    let (n,m) = get!(usize, usize);
    let ab = get!(usize, usize; m);

    let mut nodes = vec![Vec::new(); n+1];
    let mut inb = vec![0usize; n+1];
    let mut list = (1..n+1).collect::<BTreeSet<_>>();
    for (a,b) in ab {
        nodes[a].push(b);
        inb[b] += 1;
        list.remove(&b);
    }

    let mut list = list.into_iter().collect::<VecDeque<_>>();
    let mut unselected = (1..n+1).collect::<BTreeSet<_>>();

    while let Some(node) = list.pop_front() {
        unselected.remove(&node);
        for &next in &nodes[node] {
            inb[next] -= 1;
            if inb[next] == 0 {
                list.push_back(next);
            }
        }
    }

    if unselected.len() == 0 {
        println!("-1");
        return;
    }

    let mut vertexes = unselected;
    let mut edges = BTreeMap::new();
    for &i in &vertexes {
        let mut edge = Vec::new();
        for &next in &nodes[i] {
            if vertexes.contains(&next) {
                edge.push(next);
            }
        }
        edges.insert(i, edge);
    }

    fn dfs(vertex: usize, edges: &BTreeMap<usize,Vec<usize>>, visited: &mut BTreeSet<usize>) -> Option<Vec<usize>> {
        for &next in &edges[&vertex] {
            if visited.contains(&next) {
                return Some(vec![vertex]);
            }
            visited.insert(next);
            if let Some(mut res) = dfs(next, edges, visited) {
                res.push(vertex);
                return Some(res);
            }
        }
        None
    }
    let mut cycle = Vec::new();
    for &vertex in &vertexes {
        let mut visited = (vertex..vertex+1).collect::<BTreeSet<_>>();
        if let Some(r) = dfs(vertex, &edges, &mut visited) {
            cycle = r;
            break;
        }
    }
    vertexes = cycle.iter().cloned().collect::<BTreeSet<_>>();

    loop {
        let mut new = None;
        for (&vertex1, &vertex2) in cycle.iter().rev().zip(cycle.iter().rev().skip(1).chain(cycle.iter().rev().take(1))) {
            let mut edge = Vec::new();
            for &next in &edges[&vertex1] {
                if !vertexes.contains(&next) {
                    continue;
                }
                edge.push(next);
                if vertex2 != next && new.is_none() {
                    new = Some((vertex1,next));
                }
            }
            edges.insert(vertex1,edge);
        }

        if new.is_none() {
            break;
        }
        let (goal,start) = new.unwrap();
        let mut res = Vec::new();
        let mut flag = false;
        for &node in cycle.iter().rev() {
            if node == start || flag {
                flag = true;
                res.push(node);
            } else if node == goal && flag {
                flag = false;
            }
        }
        if !flag {
            for &node in cycle.iter().rev() {
                res.push(goal);
                if node == goal {
                    break;
                }
            }
        }
        cycle = res;
        vertexes = cycle.iter().cloned().collect::<BTreeSet<_>>();
    }
    println!("{}", cycle.len());
    for i in cycle {
        println!("{}", i);
    }
}