Problem: 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.

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.

Examples

Input

4 5
1 2
2 3
2 4
4 1
4 3


Output

3
1
2
4


Input

4 5
1 2
2 3
2 4
1 4
4 3


Output

-1


Input

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2


Output

4
2
3
4
5

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int M = scanner.nextInt();
    Node[] nodes = new Node[N];
    for (int i = 0; i < N; i++) nodes[i] = new Node(i);
    for (int i = 0; i < M; i++) {
      int a = scanner.nextInt() - 1;
      int b = scanner.nextInt() - 1;
      nodes[a].adjacent.add(nodes[b]);
    }

    List<Node> minLoop = null;
    for (int i = 0; i < N; i++) {
      Node src = nodes[i];
      int[] prev = new int[N];
      Arrays.fill(prev, -1);
      Queue<Node> queue = new LinkedList<>();
      for (Node n : src.adjacent) {
        prev[n.id] = src.id;
        queue.add(n);
      }
      while (!queue.isEmpty()) {
        Node n = queue.poll();
        if (n.id == src.id) {
          List<Node> path = restorePath(n, nodes, prev);
          if (minLoop == null || minLoop.size() > path.size()) minLoop = path;
          break;
        }
        for (Node a : n.adjacent) {
          if (prev[a.id] < 0) {
            prev[a.id] = n.id;
            queue.add(a);
          }
        }
      }
    }
    if (minLoop == null) {
      System.out.println(-1);
    } else {
      System.out.println(minLoop.size());
      for (Node n : minLoop) System.out.println(n.id + 1);
    }
  }

  private static List<Node> restorePath(Node node, Node[] nodes, int[] prev) {
    List<Node> res = new ArrayList<>();
    int src = node.id;
    do {
      res.add(node);
      node = nodes[prev[node.id]];
    } while (node.id != src);
    return res;
  }

  private static class Node {
    private final int id;
    private final List<Node> adjacent = new ArrayList<>();

    private Node(int id) {
      this.id = id;
    }
  }
}