Problem:
Score : 400 points

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.

Sample Input 1

5 3
-10 10 -10 10 -10

Sample Output 1

10

Paint the following squares black: the second, third and fourth squares from the left.

Sample Input 2

4 2
10 -10 -10 10

Sample Output 2

20

One possible way to obtain the maximum score is as follows:

Paint the following squares black: the first and second squares from the left.

Paint the following squares black: the third and fourth squares from the left.

Paint the following squares white: the second and third squares from the left.

Sample Input 3

1 1
-10

Sample Output 3

0

Sample Input 4

10 5
5 -4 -5 -8 -4 7 2 -4 0 7

Sample Output 4

17

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {
	
	public static void main(String[] args) throws IOException {
		final Scanner sc = new Scanner(System.in);
		
		final int N = sc.nextInt();
		final int K = sc.nextInt();
		
		long[] array = new long[N];
		for(int i = 0; i < N; i++){
			array[i] = sc.nextLong();
		}
		
		long[] in_prefix_sum = new long[N + 1];
		long[] ex_prefix_sum = new long[N + 1];
		for(int i = 0; i < N; i++){
			in_prefix_sum[i + 1] = array[i] + in_prefix_sum[i];
			ex_prefix_sum[i + 1] = Math.max(0, array[i]) + ex_prefix_sum[i];
		}
		
		long answer = 0;
		for(int first_offset = 0; first_offset <= K; first_offset++){
			final int second_index = first_offset + (N - K);
			
			final long first_sum  = Math.max(0, in_prefix_sum[first_offset]);
			final long center_sum = ex_prefix_sum[second_index] - ex_prefix_sum[first_offset];
			final long last_sum   = Math.max(0, in_prefix_sum[N] - in_prefix_sum[second_index]);
			
			//System.out.println(first_sum + " " + center_sum + " " + last_sum);
			
			answer = Math.max(answer, first_sum + center_sum + last_sum);
		}
		
		System.out.println(answer);
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;
 
		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}
 
		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}
 
		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}
 
		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public void close() throws IOException {
			br.close();
		}
	}
}