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)

use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let m: usize = it.next().unwrap().parse().unwrap();
    let mut g = vec![vec![]; n];
    let mut ig = vec![vec![]; n];
    for _ in 0..m {
        let a = it.next().unwrap().parse::<usize>().unwrap() - 1;
        let b = it.next().unwrap().parse::<usize>().unwrap() - 1;
        g[a].push(b);
        ig[b].push(a);
    }
    let mut ans = vec![0; 10000];
    for s in 0..n {
        for &t in &g[s] {
            let inf = 10000;
            let mut d = vec![inf; n];
            d[t] = 0;
            let mut q = std::collections::VecDeque::new();
            q.push_back(t);
            while let Some(v) = q.pop_front() {
                for &u in &g[v] {
                    if d[u] > d[v] + 1 {
                        d[u] = d[v] + 1;
                        q.push_back(u);
                    }
                }
            }
            if d[s] == inf {
                continue;
            }
            if ans.len() > d[s] {
                ans.clear();
                let mut now = s;
                while now != t {
                    ans.push(now);
                    for &u in &ig[now] {
                        if d[u] + 1 == d[now] {
                            now = u;
                            break;
                        }
                    }
                }
                ans.push(t);
            }
        }
    }
    if ans.len() <= n {
        println!("{}", ans.len());
        for v in ans {
            println!("{}", v + 1);
        }
    } else {
        println!("-1");
    }
}

fn main() {
    run();
}