Problem Statement

There are $N$ squares aligned in a row. The $i$-th square from the left contains an integer $a_i$.

Initially, all the squares are white. Snuke will perform the following operation some number of times:

• Select $K$ consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.

After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.

Constraints

• $1≤N≤10^5$
• $1≤K≤N$
• $a_i$ is an integer.
• $|a_i|≤10^9$

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the maximum possible score.