Leyang loves to play Candy Crush in his spare time. In level 4761 of the game, he is given a row of candies, each with a tastiness . His goal is to consume as much tastiness as possible. In a single move, he chooses a candy at position to eat, consuming tastiness. This will cause all candies within a distance to be crushed. Formally, his total tastiness increases by , and all candies are deleted and left as empty space. He may not choose a candy whose explosion reaches into empty space or over the left and right edges. If he continues to make moves until he is unable to, ~~how tasty can Leyang become~~ what is the maximum total tastiness Leyang can consume?

#### Constraints

#### Input Specification

The first line contains two numbers: , the number of candies, and , the explosion radius.

The second line contains space separated integers, each corresponding to for .

#### Output Specification

Output one integer: the maximum total tastiness Leyang can consume.

#### Sample Input

```
8 1
2 7 30 35 36 32 1 1
```

#### Sample Output

`62`

#### Explanation for Sample Output

Leyang eats the candy with tastiness `30`

, leaving `2 X X X 36 32 1 1`

(`X`

indicating empty space).

He then eats the candy with tastiness `32`

, leaving `2 X X X X X X 1`

. He cannot make any more moves so his total consumed tastiness is .

## Comments