Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Optimal Sum

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAnd here goes another problem on arrays. You are given positive integer *len* and array *a* which consists of *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n}. Let's introduce two characteristics for the given array.

- Let's consider an arbitrary interval of the array with length
*len*, starting in position*i*. Value , is the modular sum on the chosen interval. In other words, the modular sum is the sum of integers on the chosen interval with length*len*, taken in its absolute value. - Value is the optimal sum of the array. In other words, the optimal sum of an array is the maximum of all modular sums on various intervals of array with length
*len*.

Your task is to calculate the optimal sum of the given array *a*. However, before you do the calculations, you are allowed to produce no more than *k* consecutive operations of the following form with this array: one operation means taking an arbitrary number from array *a*_{i} and multiply it by -1. In other words, no more than *k* times you are allowed to take an arbitrary number *a*_{i} from the array and replace it with - *a*_{i}. Each number of the array is allowed to choose an arbitrary number of times.

Your task is to calculate the maximum possible optimal sum of the array after at most *k* operations described above are completed.

Input

The first line contains two integers *n*, *len* (1 ≤ *len* ≤ *n* ≤ 10^{5}) — the number of elements in the array and the length of the chosen subinterval of the array, correspondingly.

The second line contains a sequence consisting of *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (|*a*_{i}| ≤ 10^{9}) — the original array.

The third line contains a single integer *k* (0 ≤ *k* ≤ *n*) — the maximum allowed number of operations.

All numbers in lines are separated by a single space.

Output

In a single line print the maximum possible optimal sum after no more than *k* acceptable operations are fulfilled.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Examples

Input

5 3

0 -2 3 -5 1

2

Output

10

Input

5 2

1 -3 -10 4 1

3

Output

14

Input

3 3

-2 -5 4

1

Output

11

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/20/2019 05:02:41 (d1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|