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::collections::HashSet;
use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: expr) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let (n, m): (usize, usize) = parse!(it, 2);
    let mut g = vec![vec![]; n];
    for _ in 0..m {
        let (a, b): (usize, usize) = parse!(it, 2);
        g[a - 1].push(b - 1);
    }

    for start in 0..std::cmp::min(n, 100) {
        let mut cycles = vec![];
        let mut parents = vec![std::usize::MAX; n];
        let mut seen = vec![Unseen; n];
        seen[start] = Seen;
        dfs(&g, start, &mut seen, &mut parents, &mut cycles);
        'outer: for cycle in cycles {
            for &i in cycle.iter() {
                let mut count = 0;
                for j in g[i].iter() {
                    if cycle.contains(j) {
                        count += 1;
                    }
                }
                if count > 1 {
                    continue 'outer;
                }
            }
            println!("{}", cycle.len());
            for i in cycle {
                println!("{}", i + 1);
            }
            return;
        }
    }
    println!("{}", -1);
}

fn get_cycle(parents: &Vec<usize>, start: usize, end: usize) -> HashSet<usize> {
    let mut ret = HashSet::new();
    let mut cur = end;
    while cur != start {
        ret.insert(cur);
        cur = parents[cur];
    }
    ret.insert(start);
    ret
}

fn dfs(
    g: &Vec<Vec<usize>>,
    u: usize,
    seen: &mut Vec<State>,
    parents: &mut Vec<usize>,
    cycles: &mut Vec<HashSet<usize>>,
) {
    for &v in g[u].iter() {
        match seen[v] {
            Unseen => {
                seen[v] = Seen;
                parents[v] = u;
                dfs(g, v, seen, parents, cycles);
            }
            Seen => {
                cycles.push(get_cycle(parents, v, u));
            }
            _ => (),
        }
    }
    seen[u] = Checked;
}

#[derive(Clone, Copy, Debug)]
enum State {
    Unseen,
    Seen,
    Checked,
}
use State::*;

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}