AQT is studying directed graphs and has encountered the following problem: given a directed graph consisting of ~N~ nodes with labels ~1, 2, \dots, N~ and ~M~ edges, find a pair of vertices ~(x,y)~ such that ~x < y~ and ~y~ is reachable from ~x~. Can you help him find such a pair in the graph (or output -1 if none exists)?

Constraints

~2 \le N \le 3 \cdot 10^5~

~1 \le M \le 6 \cdot 10^5~

Subtask 1 [5%]

~2 \le N \le 5 \cdot 10^3~

~1 \le M \le 10^4~

Subtask 2 [10%]

If a directed edge connecting node ~a~ to ~b~ exists in the input, the edge connecting node ~b~ to node ~a~ is guaranteed to be in the input as well.

Subtask 3 [15%]

The graph will have no cycles.

Subtask 4 [70%]

No additional constraints.

Input Specification

The first line will contain the integers ~N~, the number of vertices in the graph, and ~M~, the number of edges in the graph.

The next ~M~ lines will each contain a directed edge in the form of ~2~ space-separated integers ~a, b~, denoting an edge from node ~a~ to ~b~. For all pairs ~(a,b)~, ~a \ne b~.

Output Specification

Output a pair ~(x,y)~ such that ~x < y~ and ~y~ is reachable from ~x~. If there exist multiple answers, output the one that maximizes ~x~, and then ~y~ if there are multiple answers with maximum ~x~.

If no answer exists, output -1 instead.

Sample Input 1

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

Sample Output 1

3 5

Explanation 1

Here is the graph given in the input:

The pairs of vertices ~(x,y)~ such that ~x < y~ and ~y~ is reachable from ~x~ are:

• ~(1,2)~
• ~(1,4)~
• ~(1,5)~
• ~(2,4)~
• ~(2,5)~
• ~(3,4)~
• ~(3,5)~

The output is thus 3 5 as ~(3,5)~ maximizes ~x~, then ~y~.

This graph also satisfies subtask 3.

Sample Input 2

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

Sample Output 2

-1

Explanation 2

Here is the graph given in the input:

There are no pairs of vertices ~(x,y)~ such that ~x < y~ and ~y~ is reachable from ~x~, so the output is -1.

This graph also satisfies subtask 3.

Sample Input 3

4 6
3 1
1 2
3 2
2 1
2 3
1 3

Sample Output 3

2 3

Explanation 3

Here is the graph given in the input:

This graph satisfies subtask 2.

Sample Input 4

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

Sample Output 4

3 5

Explanation 4

Here is the graph given in the input:

This graph satisfies subtask 3.