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)

//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

fn run() {
    input! {
        n: usize,
        m: usize,
        e: [(usize, usize); m],
    }
    let mut g = vec![vec![]; n + 1];
    for &(a, b) in e.iter() {
        g[a].push(b);
    }
    let mut ans = (n + 1, 0, 0); // 頂点数、始点、終点
    for i in 1..(n + 1) {
        let mut dp = vec![n + 2; n + 1];
        dp[i] = 0;
        let mut q = std::collections::VecDeque::new();
        q.push_back(i);
        while let Some(v) = q.pop_front() {
            for &u in g[v].iter() {
                if dp[u] > dp[v] + 1 {
                    dp[u] = dp[v] + 1;
                    q.push_back(u);
                }
            }
        }
        for j in 1..(n + 1) {
            for &u in g[j].iter() {
                if u == i {
                    ans = std::cmp::min(ans, (dp[j], i, j));
                }
            }
        }
    }
    if ans.0 > n {
        println!("-1");
        return;
    }
    let mut dp = vec![n + 2; n + 1];
    let (_, s, t) = ans;
    dp[s] = 0;
    let mut q = std::collections::VecDeque::new();
    q.push_back(s);
    while let Some(v) = q.pop_front() {
        for &u in g[v].iter() {
            if dp[u] > dp[v] + 1 {
                dp[u] = dp[v] + 1;
                q.push_back(u);
            }
        }
    }
    let mut ig = vec![vec![]; n + 1];
    for &(a, b) in e.iter() {
        ig[b].push(a);
    }
    let mut ans = vec![];
    let mut now = t;
    while now != s {
        ans.push(now);
        for &u in ig[now].iter() {
            if dp[u] < dp[now] {
                now = u;
                break;
            }
        }
    }
    ans.push(s);
    println!("{}", ans.len());
    for a in ans {
        println!("{}", a);
    }
}

fn main() {
    run();
}