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 edges: Vec<(usize, usize)> =
        (0..m).map(|_| (sc.read::<usize>()-1, sc.read::<usize>()-1)).collect();
    let child = child(true, n, &edges);
    let cycle = any_cycle(n, &child);
    if cycle == None {
        return "-1".to_string()
    }
    let cycle = cycle.unwrap();
    let mut alive = vec![false; n];
    for &v in cycle.iter() {
        alive[v] = true;
    }

    let c = cycle.len();
    let next = |i: usize, alive: &Vec<bool>| {
        let mut i = (i+1)%c;
        while !alive[cycle[i]] {
            i = (i+1)%c;
        }
        i
    };
    let mut visited = vec![false; n];
    let mut i = 0;
    'l: loop {
        let v = cycle[i];
        if visited[v] {break}
        visited[v] = true;
        for &w in child[v].iter() {
            if alive[w] && w != cycle[next(i, &alive)] {
                visited = vec![false; n];
                i = next(i, &alive);
                while w != cycle[i] {
                    alive[cycle[i]] = false;
                    i = next(i, &alive);
                }
                continue 'l;
            }
        }
        i = next(i, &alive);
    }
    writeln!(&mut buf, "{}", alive.iter().fold(0, |a, &b| if b {a+1} else {a}));
    for i in 0..n {
        if !alive[i] {continue}
        writeln!(&mut buf, "{}", i + 1);
    }

    buf
}

fn child(directed: bool, size: usize, edges: &Vec<(usize,usize)>) -> Vec<Vec<usize>> {
    let mut child = vec![Vec::new(); size];
    for &(v, w) in edges.iter() {
        child[v].push(w);
        if !directed {
            child[w].push(v);
        }
    }
    child
}

fn any_cycle(size: usize, child: &Vec<Vec<usize>>) -> Option<Vec<usize>> {
    let mut visited = vec![false; size];
    let mut path = vec![0; size];
    'search: for s in 0..size {
        let mut stack = vec![s];
        let mut depth = vec![0; size];
        let mut s_visited = false;
        while let Some(v) = stack.pop() {
            if v == s {
                if s_visited {
                    path.resize(depth[s], 0);
                    break 'search;
                } else { s_visited = true; }
            }
            path[depth[v]] = v;
            for &w in child[v].iter() {
                if visited[w] { continue; }
                visited[w] = true;
                depth[w] = depth[v] + 1;
                stack.push(w);
            }
        }
        if s == size - 1 {
            return None;
        }
    }
    Some(path)
}

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()
    }
}