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 $n$ numbers $h_1,h_2,\dots ,h_n$ where the number $h_i$ represents the height of the $i$-th skyscraper. Domagoj will photograph a contiguous subsequence of skyscrapers. To capture more of the city's beauty, he wants to photograph at least $k$ 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 $h_l,\dots ,h_r$, and with $g$ the greatest common divisor of the selected heights, then Domagoj defines the beauty of the photograph as $g\cdot (h_l+\cdots +h_r)$.

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

Input Specification

The first line contains two integers $n,k$ $(1\le k\le n\le {10}^6)$, the number of skyscrapers, and the number $k$.

The second line contains $n$ integers $h_1,h_2,\dots ,h_n$ $(1\le h_i\le {10}^6)$, the heights of the skyscrapers, in order.

Output Specification

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

Constraints

Subtask	Points	Constraints
$1$	$11$	$n,k\le 100$
$2$	$22$	$n,k\le 5000$
$3$	$27$	$h_i\le 1000$
$4$	$18$	$n,k\le 5\cdot {10}^4$
$5$	$32$	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 $(4,4,4)$, so the total beauty is $4\cdot (4+4+4)=48$.

Sample Input 2

4 1
7 3 9 4

Sample Output 2

81

Explanation for Sample Output 2

Domagoj photographed only the skyscraper $(9)$, so the total beauty is $9\cdot 9=81$.