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!
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.
Print a single line with the required number from the task.
|No additional constraints.|
Sample Input 1
6 2 2 1 4 4 4 2
Sample Output 1
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
Explanation for Sample Output 2
Domagoj photographed only the skyscraper , so the total beauty is .