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)


fn find_close(g: &Vec<Vec<usize>>, cur: usize, mut back: &mut Vec<usize>, mut visited: &mut Vec<bool>) -> Option<Vec<usize>> {
    visited[cur] = true;
    for &next in &g[cur] {
        if visited[next] {
            // FOUND
            back[next] = cur;
            let mut pos = next;
            let mut ret = vec![0usize; 0];
            loop {
                pos = back[pos];
                ret.push(pos);
                if pos == next {
                    break
                }
            }
            ret.reverse();
            return Some(ret);
        } else if back[next] == std::usize::MAX {
            back[next] = cur;
            let ret = find_close(g, next, &mut back, &mut visited);
            if ret.is_some() {
                return ret
            }
        }
    }
    visited[cur] = false;
    return None
}

fn find_close_all(g: &Vec<Vec<usize>>) -> Option<Vec<usize>> {
    let mut back = vec![std::usize::MAX; g.len()];
    let mut visited = vec![false; g.len()];

    for i in 0..g.len() {
        if back[i] != std::usize::MAX {
            continue
        }
        let ret = find_close(g, i, &mut back, &mut visited);
        if ret.is_some() {
            return ret
        }
    }
    return None
}

fn check(g: &Vec<Vec<usize>>, loops: &Vec<usize>) -> Vec<usize> {
    let mut in_loop = vec![false; g.len()];
    let mut index = vec![0usize; g.len()];
    for (i, &v) in loops.iter().enumerate() {
        in_loop[v] = true;
        index[v] = i;
    }
    for &v in loops {
        for &u in &g[v] {
            if in_loop[u] {
                if (index[v] + 1) % loops.len() != index[u] {
                    let mut next_loop = vec![0usize; 0];
                    let mut cur = index[u];
                    while cur != index[v] {
                        next_loop.push(loops[cur]);
                        cur = (cur + 1) % loops.len();
                    }
                    next_loop.push(loops[cur]);
                    assert!(next_loop.len() < loops.len());
                    return check(g, &next_loop);
                }
            }
        }
    }
    return loops.clone()
}

fn main() {
    let (n, m) = {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let v: Vec<usize> = line.split_whitespace().map(|a| a.parse().unwrap()).collect();
        (v[0], v[1])
    };
    let mut g = vec![vec![0usize; 0]; n];
    for _ in 0..m {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let v: Vec<usize> = line.split_whitespace().map(|a| a.parse().unwrap()).collect();
        g[v[0] - 1].push(v[1] - 1);
    }
    let loopc = find_close_all(&g);
    if loopc.is_none() {
        println!("-1");
        return;
    } else {
        let ret = check(&g, &loopc.unwrap());
        println!("{}", ret.len());
        for v in ret {
            println!("{}", v + 1);
        }
    }
}