Problem Statement  
The RowGame is a oneplayer game in which a single piece is moved across a board. The board consists of N squares arranged in a row, numbered 1 through N, from left to right. Each square has an associated value. Initially, the piece is on square 1, and the current direction is right. On each turn, the player moves zero or more squares in the current direction. The direction is then reversed for the next turn. Scoring works as follows. Initially the player's score is 0. Each time the player moves from square A to square B, the sum of the values of each square between A and B, inclusive, is added to his score. Values can be negative, and the player is never allowed to make a move that will cause his score to drop below zero. You are given a int[] board, where the ith element (0indexed) is the value of square (i+1). Return the maximum score that can be attained if the player is allowed to make at most k moves.  
Definition  
 
Constraints  
  board will contain between 1 and 50 elements, inclusive.  
  Each element of board will be between 400000000 and 400000000, inclusive.  
  k will be between 1 and 400000000, inclusive.  
Examples  
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