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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
  "bufio"
  "fmt"
  "os"
  "strconv"
  "strings"
)

func main() {
  input := Input{bufio.NewReaderSize(os.Stdin,100)}
  n,m := input.NextInts()
  g := make([][]int,n)
  r := make([][]int,n)
  for i:=0;i<m;i++ {
    a,b := input.NextInts()
    g[a-1] = append(g[a-1],b-1)
    r[b-1] = append(r[b-1],a-1)
  }
  u := make([]int,n)
  s := make([]bool,n)
  var dfs1 func(int,int) (int,int)
  dfs1 = func(x,d int) (int,int) {
    if u[x] >= 0 && s[x] { return x,d }
    u[x] = d
    s[x] = true
    ret1,ret2 := -1,1<<30
    for _,y := range g[x] {
      tmp1,tmp2 := dfs1(y,d+1)
      if tmp1 >= 0 && tmp2 < ret2 { ret1,ret2 = tmp1,tmp2 }
    }
    s[x] = false
    return ret1,ret2
  }
  var dfs2 func(int,int,int)
  dfs2 = func(x,t,d int) {
    if x == t && u[x] == d { return }
    fmt.Println(x+1)
    for _,y := range r[x] {
      if u[y] == d-1 { dfs2(y,t,d-1);return }
    }
  }
  min := 1<<30
  ans := -1
  for i:=0;i<n;i++ {
    for j:=0;j<n;j++ { u[j] = -1;s[j] = false }
    x,d := dfs1(i,0)
    if x < 0 { continue }
    if min > d-u[x] {
      min = d-u[x]
      ans = i
    }
  }
  if ans < 0 { fmt.Println(-1);return }
  for i:=0;i<n;i++ { u[i] = -1;s[i] = false }
  fmt.Println(min)
  x,d := dfs1(ans,0)
  dfs2(x,x,d)
}

type Input struct { reader *bufio.Reader }
func(i *Input) NextLine() string {
  var buffer []byte
  for {
    line,isPrefix,err := i.reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer,line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func(i *Input) NextInts() (int,int) {
  s := strings.Fields(i.NextLine())
  x,_ := strconv.Atoi(s[0])
  y,_ := strconv.Atoi(s[1])
  return x,y
}