Domagoj is in the big city of London! Right now, there is a sequence of tall skyscrapers in front of him and he wants to take a photograph to remember the moment.

The sequence of skyscrapers can be represented as a sequence of numbers where the number represents the height of the -th skyscraper. Domagoj will photograph a contiguous subsequence of skyscrapers. To capture more of the city's beauty, he wants to photograph at least skyscrapers.

Domagoj has a strange sense of beauty of a photograph. He is very happy when there are tall skyscrapers in the photograph, but he is even happier when their heights have a large common divisor! If we label the heights of the contiguous skyscrapers on the photograph with , and with the greatest common divisor of the selected heights, then Domagoj defines the beauty of the photograph as .

Help Domagoj determine the beauty of the most beautiful photograph with at least skyscrapers!

#### Input Specification

The first line contains two integers , the number of skyscrapers, and the number .

The second line contains integers , the heights of the skyscrapers, in order.

#### Output Specification

Print a single line with the required number from the task.

#### Constraints

Subtask | Points | Constraints |
---|---|---|

No additional constraints. |

#### Sample Input 1

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

#### Sample Output 1

`48`

#### Explanation for Sample Output 1

Domagoj photographed skyscrapers , so the total beauty is .

#### Sample Input 2

```
4 1
7 3 9 4
```

#### Sample Output 2

`81`

#### Explanation for Sample Output 2

Domagoj photographed only the skyscraper , so the total beauty is .

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