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.

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 ${v_1, v_2, \ldots, v_K$}.$v_1, v_2, \ldots, v_K$ does not matter.)
If there are multiple subgraphs of G that satisfy the condition, printing any of them is accepted.

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.

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

见题面 Input 部分

见题面 Output 部分