Maximum Shade

Given an array of integers representing the shade produced by each tree, determine the maximum sum of any ( k ) consecutive trees. The sum is calculated using a sliding window technique.

Mathematically, the problem is formulated as follows:
[ \text{maxShade}(A,k)=\begin{cases} \max_{1 \leq i \leq n-k+1} \sum_{j=i}^{i+k-1}A_j, & \text{if } k \leq n \ 0, & \text{if } k > n \end{cases} ]

If the array is empty or the number of trees is less than ( k ), the output should be 0.

inputFormat

The input is given via standard input (stdin).

The first line contains two integers ( n ) and ( k ), where ( n ) is the number of trees (the length of the array) and ( k ) is the number of consecutive trees to consider.
The second line contains ( n ) space-separated integers representing the shade of each tree. If ( n = 0 ), the second line will be empty.

outputFormat

Output a single integer to standard output (stdout): the maximum sum of the shades from any ( k ) consecutive trees. If there is no valid segment (i.e., if ( k > n ) or the array is empty), output 0.## sample

6 3
2 1 5 1 3 2

9