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$\}.$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

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