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: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;


public class Main {
  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int N = sc.nextInt();
    int K = sc.nextInt();
    long[] a = new long[N + 1];
    for (int i = 1; i <= N; i ++) {
      a[i] = sc.nextLong();
    }

    System.out.println(solve(N, K, a));
    
  }

  private static long solve(int N, int K, long[] a) {
    long[] sum = new long[N + 1];
    long[] asum = new long[N + 1];
    for (int i = 1; i <= N; i ++) {
      sum[i] = sum[i - 1] + a[i];
      if (a[i] >= 0) {
        asum[i] = asum[i - 1] + a[i];
      } else {
        asum[i] = asum[i - 1];
      }
    }
    
    long ret = Long.MIN_VALUE;;
    
    
    for (int i = 1; i <= N - K + 1; i ++) {
      long A = asum[i - 1];
      long B = sum[i + K - 1] - sum[i - 1];
      long C = asum[N] - asum[i + K - 1];
      long now = A + B + C;
      ret = Math.max(ret, now);
    }
    
    for (int i = 1; i <= N - K + 1; i ++) {
      long A = asum[i - 1];
      long C = asum[N] - asum[i + K - 1];
      long now = A + C;
      ret = Math.max(ret, now);
    }
    return ret;
  }
}


class BIT {
  private long[] array;
  private int n;

  public BIT(int n) {
    this.array = new long[n + 1];
    this.n = n;
  }

  public void add(int a, long w) {
    for (int i = a; i <= n; i += (i & -i)) {
      array[i] += w;
    }
  }

  public long sum(int a) {
    long ret = 0;
    for (int i = a; i > 0; i -= (i & -i)) {
      ret += array[i];
    }
    return ret;
  }

  public long sum(int a, int b) {
    return a == 0 ? sum(b) : (sum(b) - sum(a - 1));
  }

}


class FastScanner {
  public static String debug = null;

  private final InputStream in = System.in;
  private int ptr = 0;
  private int buflen = 0;
  private byte[] buffer = new byte[1024];
  private boolean eos = false;

  private boolean hasNextByte() {
    if (ptr < buflen) {
      return true;
    } else {
      ptr = 0;
      try {
        if (debug != null) {
          buflen = debug.length();
          buffer = debug.getBytes();
          debug = "";
          eos = true;
        } else {
          buflen = in.read(buffer);
        }
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (buflen < 0) {
        eos = true;
        return false;
      } else if (buflen == 0) {
        return false;
      }
    }
    return true;
  }

  private int readByte() {
    if (hasNextByte())
      return buffer[ptr++];
    else
      return -1;
  }

  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }

  private void skipUnprintable() {
    while (hasNextByte() && !isPrintableChar(buffer[ptr]))
      ptr++;
  }

  public boolean isEOS() {
    return this.eos;
  }

  public boolean hasNext() {
    skipUnprintable();
    return hasNextByte();
  }

  public String next() {
    if (!hasNext())
      throw new NoSuchElementException();
    StringBuilder sb = new StringBuilder();
    int b = readByte();
    while (isPrintableChar(b)) {
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }

  public long nextLong() {
    if (!hasNext())
      throw new NoSuchElementException();
    long n = 0;
    boolean minus = false;
    int b = readByte();
    if (b == '-') {
      minus = true;
      b = readByte();
    }
    if (b < '0' || '9' < b) {
      throw new NumberFormatException();
    }
    while (true) {
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
      b = readByte();
    }
  }

  public int nextInt() {
    return (int) nextLong();
  }

  public long[] nextLongList(int n) {
    return nextLongTable(1, n)[0];
  }

  public int[] nextIntList(int n) {
    return nextIntTable(1, n)[0];
  }

  public long[][] nextLongTable(int n, int m) {
    long[][] ret = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ret[i][j] = nextLong();
      }
    }
    return ret;
  }

  public int[][] nextIntTable(int n, int m) {
    int[][] ret = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ret[i][j] = nextInt();
      }
    }
    return ret;
  }
}