A row of n tiles is numbered 0 to n-1; tile i holds an integer token value a[i] (possibly negative). A player starts on tile 0 and must finish on tile n-1. From tile i the player may jump forward to any tile j with i + 1 <= j <= i + k. The score of a run is the sum of the token values of all tiles the player lands on, including the start tile 0 and the end tile n-1.
Report the maximum possible score.
Input format
Line 1: two integers n and k.
Line 2: n space-separated integers, the token values a[0..n-1].
Output format
A single integer: the maximum achievable score.
Constraints
- 1 <= k <= n <= 100000
- -1000000000 <= a[i] <= 1000000000