Pure

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

inputFormat

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

outputFormat

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

样例

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

4
2
3
4
5

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