AQT is studying directed graphs and has encountered the following problem: given a directed graph consisting of nodes with labels and edges, find a pair of vertices such that and is reachable from . Can you help him find such a pair in the graph (or output if none exists)?

#### Constraints

##### Subtask 1 [5%]

##### Subtask 2 [10%]

If a directed edge connecting node to exists in the input, the edge connecting node to node 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 , the number of vertices in the graph, and , the number of edges in the graph.

The next lines will each contain a directed edge in the form of space-separated integers , denoting an edge from node to . For all pairs , .

#### Output Specification

Output a pair such that and is reachable from . **If there exist multiple answers**, output the one that maximizes , and then if there are multiple answers with maximum .

If no answer exists, output instead.

#### Sample Input 1

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

#### Sample Output 1

`3 5`

#### Explanation

Here is the graph given in the input:

The pairs of vertices such that and is reachable from are:

The output is thus `3 5`

as maximises , then .

This graph also satisfies subtask .

#### Sample Input 2

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

#### Sample Output 2

`-1`

#### Explanation

Here is the graph given in the input:

There are no pairs of vertices such that and is reachable from so the output is `-1`

.

This graph also satisfies subtask .

#### Sample Input 3

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

#### Sample Output 3

`2 3`

#### Explanation

Here is the graph given in the input:

This graph satisfies subtask .

#### Sample Input 4

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

#### Sample Output 4

`3 5`

#### Explanation

Here is the graph given in the input:

This graph satisfies subtask .

## Comments