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: Time Limit Exceeded)

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut graph = vec![vec![]; n];
    for _ in 0..m {
        let a = sc.read::<usize>() - 1;
        let b = sc.read::<usize>() - 1;
        graph[a].push(b);
    }

    let mut prohibited = vec![0; n];
    let mut vis = vec![false; n];
    for start in 0..n {
        let mut memo = None;
        if naive_dfs(start, &graph, &mut prohibited, &mut vis, start, &mut memo) {
            let ans = vis
                .into_iter()
                .enumerate()
                .filter(|&(_, v)| v)
                .map(|(i, _)| i + 1)
                .collect::<Vec<_>>();
            println!("{}", ans.len());
            for ans in ans.into_iter() {
                println!("{}", ans);
            }
            return;
        }

        if let Some(start) = memo {
            if naive_dfs(start, &graph, &mut prohibited, &mut vis, start, &mut memo) {
                let ans = vis
                    .into_iter()
                    .enumerate()
                    .filter(|&(_, v)| v)
                    .map(|(i, _)| i + 1)
                    .collect::<Vec<_>>();
                println!("{}", ans.len());
                for ans in ans.into_iter() {
                    println!("{}", ans);
                }
                return;
            }
            unreachable!()
        }
    }
    println!("-1");
}

fn naive_dfs(
    v: usize,
    graph: &Vec<Vec<usize>>,
    prohibited: &mut Vec<usize>,
    vis: &mut Vec<bool>,
    start: usize,
    memo: &mut Option<usize>,
) -> bool {
    let next_vis_count = graph[v].iter().filter(|&&next| vis[next]).count();
    let next_start = graph[v].contains(&start);
    if next_vis_count == 1 && next_start {
        vis[v] = true;
        return true;
    }
    if next_vis_count == 1 {
        *memo = Some(v);
        return false;
    }
    if next_vis_count > 0 {
        return false;
    }

    vis[v] = true;
    for &next in graph[v].iter() {
        prohibited[next] += 1;
    }
    for &next in graph[v].iter() {
        prohibited[next] -= 1;
        if prohibited[next] == 0 {
            if naive_dfs(next, graph, prohibited, vis, start, memo) {
                return true;
            }
        }
        prohibited[next] += 1;
    }

    for &next in graph[v].iter() {
        prohibited[next] -= 1;
    }
    vis[v] = false;
    false
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}