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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused_imports)]
use {
   proconio::{fastout, input, marker::*},
   std::cmp::*,
   std::collections::*,
};

trait Monoid {
   fn unit() -> Self;
}
#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
enum MinInt {
   Val(i64),
   Maximal,
}
impl MinInt {
   fn unwrap(self) -> i64 {
      if let Self::Val(x) = self {
         x
      } else {
         panic!();
      }
   }
}
impl std::ops::Mul for MinInt {
   type Output = Self;
   fn mul(self, other: Self) -> Self {
      if self < other {
         self
      } else {
         other
      }
   }
}
impl Monoid for MinInt {
   fn unit() -> Self { MinInt::Maximal }
}

use MinInt::*;

#[fastout]
fn main() {
   input! {
      n: usize,
      m: usize,
      ab: [(Usize1, Usize1); m]
   }
   let mut to = vec![vec![]; n];
   let mut from = vec![vec![]; n];
   for (a, b) in ab {
      to[a].push(b);
      from[b].push(a);
   }
   for s in 0..n {
      if to[s].len() * from[s].len() == 0 {
         continue;
      }

      let mut q = VecDeque::new();
      q.push_back(s);
      let mut d = vec![Maximal; n];
      d[s] = Val(0);
      while let Some(v) = q.pop_front() {
         for &u in to[v].iter() {
            if d[u] == Maximal {
               d[u] = Val(d[v].unwrap() + 1);
               q.push_back(u);
            }
         }
      }
      for &t in from[s].iter() {
         if let Val(k) = d[t] {
            println!("{}", k + 1);
            let mut v = t;
            let mut x = k;
            println!("{}", v+1);
            while x > 0 {
               for &u in from[v].iter() {
                  if d[u] == Val(x - 1) {
                     println!("{}", u + 1);
                     v = u;
                     x -= 1;
                     break;
                  }
               }
            }
            return;
         }
      }
   }
   println!("-1");
}