And here goes another problem on arrays. You are given positive integer len and array a which consists of n integers a1, a2, ..., an. 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 <image>, 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 <image> 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 ai and multiply it by -1. In other words, no more than k times you are allowed to take an arbitrary number ai from the array and replace it with  - ai. 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 ≤ 105) — 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 a1, a2, ..., an (|ai| ≤ 109) — 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
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
	
	class Pair implements Comparable<Pair> {
		int val, id;
		
		Pair(int val, int id) {
			this.val = val;
			this.id = id;
		}
		
		@Override
		public int compareTo(Pair p) {
			if (val != p.val)
				return val < p.val ? -1 : 1;
			if (id != p.id)
				return id < p.id ? -1 : 1;
			return 0;
		}
	}
	
	void solve() throws Exception {
		int n = sc.nextInt();
		int len = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		int k = sc.nextInt();
		TreeSet<Pair> pmx = new TreeSet<Pair>();
		TreeSet<Pair> po = new TreeSet<Pair>();
		TreeSet<Pair> nmx = new TreeSet<Pair>();
		TreeSet<Pair> no = new TreeSet<Pair>();
		long ans = Long.MIN_VALUE;
		long spmx = 0, spo = 0, snmx = 0, sno = 0;
		for (int i = 0; i < len; i++) {
			if (a[i] < 0) {
				int x = -a[i];
				if (nmx.size() < k) {
					nmx.add(new Pair(x, i));
					snmx += x;
				} else {
					nmx.add(new Pair(x, i));
					snmx += x;
					Pair p = nmx.pollFirst();
					snmx -= p.val;
					sno += p.val;
					no.add(p);
				}
			} else {
				int x = a[i];
				if (pmx.size() < k) {
					pmx.add(new Pair(x, i));
					spmx += x;
				} else {
					pmx.add(new Pair(x, i));
					spmx += x;
					Pair p = pmx.pollFirst();
					spmx -= p.val;
					spo += p.val;
					po.add(p);
				}				
			}
		}
		ans = spmx + snmx + max(spo, sno) - min(spo, sno);
		for (int i = len; i < n; i++) {
			int j = i - len;
			if (a[j] < 0) {
				int x = -a[j];
				if (nmx.contains(new Pair(x, j))) {
					snmx -= x;
					nmx.remove(new Pair(x, j));
					if (no.size() > 0) {
						Pair p = no.pollLast();
						sno -= p.val;
						nmx.add(p);
						snmx += p.val;
					}
				} else {
					no.remove(new Pair(x, j));
					sno -= x;
				}
			} else {
				int x = a[j];
				if (pmx.contains(new Pair(x, j))) {
					spmx -= x;
					pmx.remove(new Pair(x, j));
					if (po.size() > 0) {
						Pair p = po.pollLast();
						spo -= p.val;
						pmx.add(p);
						spmx += p.val;
					}
				} else {
					po.remove(new Pair(x, j));
					spo -= x;
				}
			}
			if (a[i] < 0) {
				int x = -a[i];
				if (nmx.size() < k) {
					nmx.add(new Pair(x, i));
					snmx += x;
				} else {
					nmx.add(new Pair(x, i));
					snmx += x;
					Pair p = nmx.pollFirst();
					snmx -= p.val;
					sno += p.val;
					no.add(p);
				}
			} else {
				int x = a[i];
				if (pmx.size() < k) {
					pmx.add(new Pair(x, i));
					spmx += x;
				} else {
					pmx.add(new Pair(x, i));
					spmx += x;
					Pair p = pmx.pollFirst();
					spmx -= p.val;
					spo += p.val;
					po.add(p);
				}				
			}
			ans = max(ans, spmx + snmx + max(spo, sno) - min(spo, sno));
		}
		out.println(ans);
	}
	
	final String INPUT_FILE = "";
	final String OUTPUT_FILE = "";
	
	BufferedReader in;
	PrintWriter out;
	FastScanner sc;
	
	static Throwable throwable;
	
	public static void main(String[] args) throws Throwable {
		Thread thread = new Thread(null, new Solution(), "", (1 << 26));
		thread.start();
		thread.join();
		thread.run();
		if (throwable != null)
			throw throwable;
	}
	
	@Override
	public void run() {
		try {
			if (INPUT_FILE.equals(""))
				in = new BufferedReader(new InputStreamReader(System.in));
			else
				in = new BufferedReader(new FileReader(INPUT_FILE));
			if (OUTPUT_FILE.equals(""))
				out = new PrintWriter(System.out);
			else
				out = new PrintWriter(new FileWriter(OUTPUT_FILE));
			sc = new FastScanner(in);
			solve();
		} catch (Exception e) {
			throwable = e;
		} finally {
			out.close();
		}
	}
}

class FastScanner {
	BufferedReader reader;
	StringTokenizer strTok;
	
	FastScanner(BufferedReader reader) {
		this.reader = reader;
	}
	
	public String nextToken() throws Exception {
		while (strTok == null || !strTok.hasMoreTokens()) {
			strTok = new StringTokenizer(reader.readLine());
		}
		return strTok.nextToken();
	}
	
	public boolean EOF() throws Exception {
		if (strTok != null && strTok.hasMoreTokens()) {
			return false;
		} else {
			String line = reader.readLine();
			if (line == null)
				return true;
			strTok = new StringTokenizer(line);
			return false;
		}
	}
	
	public int nextInt() throws Exception {
		return Integer.parseInt(nextToken());
	}
	
	public double nextDouble() throws Exception {
		return Double.parseDouble(nextToken());
	}
	
	public long nextLong() throws Exception {
		return Long.parseLong(nextToken());
	}
}
