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(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn bfs(start: usize, edges: &Vec<Vec<usize>>) -> Option<(i64, Vec<usize>)> {
    let mut que = VecDeque::new();
    que.push_back(start);
    let mut dist = vec![std::i64::MAX; edges.len()];
    dist[start] = 0;
    let mut from = vec![std::usize::MAX; edges.len()];
    while let Some(cur) = que.pop_front() {
        for &to in edges[cur].iter() {
            if dist[to] <= std::i64::MAX {
                continue;
            }
            dist[to] = dist[cur] + 1;
            que.push_back(to);
            from[to] = cur;
        }
    }
    let mut min_dist = std::i64::MAX;
    let mut goal = std::usize::MAX;
    for cur in 0..edges.len() {
        for &to in edges[cur].iter() {
            if start == to {
                if dist[cur] < min_dist {
                    min_dist = dist[cur];
                    goal = cur;
                }
                break;
            }
        }
    }
    if min_dist == std::i64::MAX {
        return None;
    }

    // back_trace
    let mut root = vec![start, goal];
    let mut cur = goal;
    while from[cur] != start {
        root.push(from[cur]);
        cur = from[cur];
    }
    root.push(start);
    root.reverse();
    Some((min_dist + 1, root))
}

fn main() {
    let v = read_vec::<usize>();
    let (n, m) = (v[0], v[1]);
    let mut edges = vec![vec![]; n];
    for i in 0..m {
        let v = read_vec::<usize>();
        let (a, b) = (v[0] - 1, v[1] - 1);
        edges[a].push(b);
    }

    let mut min_cycle = std::i64::MAX;
    let mut min_root = vec![];
    for i in 0..n {
        if let Some((cycle, root)) = bfs(i, &edges) {
            if cycle < min_cycle {
                min_cycle = cycle;
                min_root = root;
            }
        }
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}