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::{
    i64,
    f64,
    cmp,
};

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };

    (stream = $s:expr, $($r:tt)*) => {
        input_inner!{$s, $($r)*}
    };

    ($($r:tt)*) => {
        use std::io::*;
        let mut stream = stdin();
        let stream = &mut stream;
        input_inner!{stream, $($r)*}
    };
}

macro_rules! input_inner {
    ($stream:expr) => {};
    ($stream:expr, ) => {};

    ($stream:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($stream, $t);
        input_inner!{$stream $($r)*}
    };
}

macro_rules! read_value {
    ($stream:expr, ( $($t:tt),* )) => {
        ( $(read_value!($stream, $t)),* )
    };

    ($stream:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($stream, $t)).collect::<Vec<_>>()
    };

    ($stream:expr, chars) => {
        read_value!($stream, String).chars().collect::<Vec<char>>()
    };

    ($stream:expr, usize1) => {
        read_value!($stream, usize) - 1
    };

    ($stream:expr, $t:ty) => {
        $stream.by_ref().bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<$t>()
            .expect("Parse error")
    };
}

#[derive(Clone)]
enum Status {
    New,
    Active,
    Finished,
}

fn is_acyclic_dfs(v: usize, e: &Vec<Vec<usize>>, status: &mut Vec<Status>) -> Option<Vec<usize>> {
    status[v] = Status::Active;
    let mut path = None;
    for &w in &e[v] {
        match status[w] {
            Status::Active => {path = Some(vec![w, v]); break;},
            Status::New => {
                if let Some(mut p) = is_acyclic_dfs(w, e, status) {
                    if p[0] != *p.last().unwrap() {
                        p.push(v);
                    }
                    path = Some(p);
                    break;
                }
            },
            Status::Finished => {}
        }
    }

    status[v] = Status::Finished;
    path
}

fn main() {
    input!{n: usize, m: usize};
    let mut e: Vec<Vec<usize>> = vec![vec![]; n];
    for _ in 0 .. m {
        input!{a: usize1, b: usize1};
        e[a].push(b);
    }

    let mut status: Vec<Status> = vec![Status::New; n];
    for v in 0 .. n {
        match status[v] {
            Status::New => {
                if let Some(path) = is_acyclic_dfs(v, &e, &mut status) {
                    let l = path.len();
                    println!("{}", l - 1);
                    for i in path[.. (l - 1)].iter().rev() {
                        println!("{}", i + 1);
                    }
                    return;
                }
            },
            _ => {}
        }
    }
    println!("-1")
}