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];
    let mut d = vec![0; 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);
        d[b] += 1;
    }
    let mut del = vec![false; n];
    loop {
        let mut update = false;
        for i in 0..n {
            if del[i] {
                continue;
            }
            let mut go = false;
            for &u in &g[i] {
                if !del[u] {
                    go = true;
                }
            }
            if d[i] == 0 || !go {
                del[i] = true;
                update = true;
                for &u in &g[i] {
                    d[u] -= 1;
                }
            }
        }
        if !update {
            break;
        }
    }
    if del.iter().all(|v| *v) {
        println!("-1");
        return;
    }
    loop {
        let mut update = false;
        for i in 0..n {
            if del[i] {
                continue;
            }
            let mut d = vec![10000; n];
            let mut q = std::collections::VecDeque::new();
            d[i] = 0;
            q.push_back(i);
            let mut s = i;
            let mut t = i;
            'outer: while let Some(v) = q.pop_front() {
                for &u in &g[v] {
                    if del[u] {
                        continue;
                    }
                    if d[u] > d[v] + 1 {
                        d[u] = d[v] + 1;
                        q.push_back(u);
                    } else if d[u] < d[v] {
                        s = u;
                        t = v;
                        break 'outer;
                    }
                }
            }
            let mut dp = vec![vec![]; n];
            dp[s].push(s);
            let mut q = std::collections::VecDeque::new();
            q.push_back(s);
            while let Some(v) = q.pop_front() {
                for &u in &g[v] {
                    if del[u] || d[u] != d[v] + 1 || dp[u].len() > 0 {
                        continue;
                    }
                    let mut a = dp[v].clone();
                    dp[u].append(&mut a);
                    dp[u].push(u);
                    q.push_back(u);
                }
            }
            let mut next = vec![true; n];
            for &v in dp[t].iter() {
                next[v] = false;
            }
            for i in 0..n {
                if !del[i] && next[i] {
                    del[i] = true;
                    update = true;
                }
            }
        }
        if !update {
            break;
        }
    }
    let cnt = del.iter().filter(|p| !**p).count();
    println!("{}", cnt);
    for i in 0..n {
        if !del[i] {
            println!("{}", i + 1);
        }
    }
}

fn main() {
    run();
}