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(dead_code)]
#![allow(unused_must_use)]

fn solve(src: &str) -> String {
    use std::fmt::Write;
    let mut buf = String::new();
    let mut sc = Scanner::from_str(&src);

    let n : usize = sc.read();
    let m : usize = sc.read();
    let e : Vec<Vec<usize>> = {
        let mut e = vec![Vec::new(); n];
        for _ in 0..m {
            let a: usize = sc.read();
            let b: usize = sc.read();
            e[a-1].push(b-1);
        }
        e
    };

    for st in 0..n {
        let mut path = vec![0; n];
        let mut stack = vec![st];
        let mut visited = vec![false; n];
        let mut d = vec![0; n];
        let mut ok = false;
        let mut not_f = false;
        while let Some(v) = stack.pop() {
            if v == st && not_f {
                ok = true;
                break
            }
            not_f = true;
            path[d[v]] = v;
            for &w in &e[v] { if !visited[w] {
                visited[w] = true;
                d[w] = d[v]+1;
                stack.push(w);
            }}
        }
        if ok {
            writeln!(&mut buf, "{}", d[st]);
            for i in 0..d[st] {
                writeln!(&mut buf, "{}", path[i]+1);
            }
            return buf
        }
    }

    "-1".to_string()
}

fn check(ans: &str, input: &str, out: &str) {
    let mut ans = Scanner::from_str(ans);
    let mut input = Scanner::from_str(input);
    let mut out = Scanner::from_str(out);

    let n: isize = ans.read();
    assert_eq!(n, out.read::<isize>());
    if n == -1 { return () }
    let n = n as usize;
    let mut ans: Vec<usize> = ans.vec(n);
    ans.sort();
    let mut out: Vec<usize> = out.vec(n);
    assert_eq!(&ans, &out);
}

#[test]
fn test() {
    let s = r"4 5
1 2
2 3
2 4
4 1
4 3";
check(&solve(s),s,r"3
1
2
4");
let s = r"4 5
1 2
2 3
2 4
1 4
4 3";
check(&solve(s),s,r"-1");
let s = r"6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2";
check(&solve(s),s,r"4
2
3
4
5");
}

fn main() {
    let mut buf = String::new();
    use std::io::Read;
    std::io::stdin().read_to_string(&mut buf);
    use std::io::Write;
    std::io::stdout().write_all(solve(&buf).as_bytes());
}

struct Scanner<I>{
    src: I
}

impl<'a> Scanner<std::str::SplitWhitespace<'a>> {
    fn from_str(src: &'a str) -> Self {
        Scanner { src: src.split_whitespace() }
    }
}

impl<'a, I> Scanner<I> where I: std::iter::Iterator<Item = &'a str>{
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.src.next().unwrap().parse().ok().expect("Parse error")
    }
    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    fn chars(&mut self) -> Vec<char> {
        self.src.next().unwrap().chars().collect()
    }
}