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.util.NavigableSet;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.SortedSet;
import java.util.Comparator;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Random;
import java.io.Writer;
import java.util.Collection;
import java.util.List;
import java.io.IOException;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.util.Set;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		int count = in.readInt();
		int length = in.readInt();
		final int[] numbers = IOUtils.readIntArray(in, count);
		int canConvert = in.readInt();
		TreapSet<Integer> positive = new TreapSet<Integer>(new Comparator<Integer>() {
			public int compare(Integer o1, Integer o2) {
				int value = numbers[o2] - numbers[o1];
				if (value != 0)
					return value;
				return o1 - o2;
			}
		});
		TreapSet<Integer> negative = new TreapSet<Integer>(new Comparator<Integer>() {
			public int compare(Integer o1, Integer o2) {
				int value = numbers[o1] - numbers[o2];
				if (value != 0)
					return value;
				return o1 - o2;
			}
		});
		long positiveSum = 0;
		long negativeSum = 0;
		long topPositiveSum = 0;
		long topNegativeSum = 0;
		for (int i = 0; i < length; i++) {
			if (numbers[i] > 0) {
				positiveSum += numbers[i];
				positive.add(i);
				if (positive.headSet(i, false).size() < canConvert) {
					topPositiveSum += numbers[i];
					if (positive.size() > canConvert)
						topPositiveSum -= numbers[positive.get(canConvert)];
				}
			} else if (numbers[i] < 0) {
				negativeSum -= numbers[i];
				negative.add(i);
				if (negative.headSet(i, false).size() < canConvert) {
					topNegativeSum -= numbers[i];
					if (negative.size() > canConvert)
						topNegativeSum += numbers[negative.get(canConvert)];
				}
			}
		}
		long answer = Math.max(positiveSum - negativeSum + 2 * topNegativeSum, negativeSum - positiveSum + 2 * topPositiveSum);
		for (int i = length; i < count; i++) {
			if (numbers[i - length] > 0) {
				positiveSum -= numbers[i - length];
				if (positive.headSet(i - length, false).size() < canConvert) {
					topPositiveSum -= numbers[i - length];
					if (positive.size() > canConvert)
						topPositiveSum += numbers[positive.get(canConvert)];
				}
				positive.remove(i - length);
			} else if (numbers[i - length] < 0) {
				negativeSum += numbers[i - length];
				if (negative.headSet(i - length, false).size() < canConvert) {
					topNegativeSum += numbers[i - length];
					if (negative.size() > canConvert)
						topNegativeSum -= numbers[negative.get(canConvert)];
				}
				negative.remove(i - length);
			}
			if (numbers[i] > 0) {
				positiveSum += numbers[i];
				positive.add(i);
				if (positive.headSet(i, false).size() < canConvert) {
					topPositiveSum += numbers[i];
					if (positive.size() > canConvert)
						topPositiveSum -= numbers[positive.get(canConvert)];
				}
			} else if (numbers[i] < 0) {
				negativeSum -= numbers[i];
				negative.add(i);
				if (negative.headSet(i, false).size() < canConvert) {
					topNegativeSum -= numbers[i];
					if (negative.size() > canConvert)
						topNegativeSum += numbers[negative.get(canConvert)];
				}
			}
			answer = Math.max(answer, Math.max(positiveSum - negativeSum + 2 * topNegativeSum, negativeSum - positiveSum + 2 * topPositiveSum));
		}
		out.printLine(answer);
	}
}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public static boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}

	public void close() {
		writer.close();
	}

	}

class IOUtils {

	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}

	}

class TreapSet<K> implements NavigableSet<K> {
	protected static final Random rnd = new Random(239);

	protected final Node nullNode;
	protected final Comparator<? super K> comparator;
	protected Node root;
	private final K from;
	private final K to;
	private final boolean fromInclusive;
	private final boolean toInclusive;

	public TreapSet() {
		this((Comparator<? super K>)null);
	}

	public TreapSet(Comparator<? super K> comparator) {
		this(null, null, false, false, comparator, null, null);
	}

	public TreapSet(Iterable<? extends K> collection) {
		this(collection, null);
	}

	public TreapSet(Iterable<? extends K> collection, Comparator<? super K> comparator) {
		this(comparator);
		addAll(collection);
	}

	protected TreapSet(K from, K to, boolean fromInclusive, boolean toInclusive, Comparator<? super K> comparator, Node root, Node nullNode) {
		this.comparator = comparator;
		this.from = from;
		this.to = to;
		this.fromInclusive = fromInclusive;
		this.toInclusive = toInclusive;
		if (nullNode == null)
			nullNode = new NullNode();
		if (root == null)
			root = nullNode;
		this.root = root;
		this.nullNode = nullNode;
	}

	public boolean addAll(Iterable<? extends K> collection) {
		boolean result = false;
		for (K element : collection)
			result |= add(element);
		return result;
	}

	public K lower(K k) {
		Node target = root.lower(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	private boolean belongs(K key) {
		int valueFrom = compare(from, key);
		int valueTo = compare(key, to);
		return (valueFrom < 0 || valueFrom == 0 && fromInclusive) && (valueTo < 0 || valueTo == 0 && toInclusive);
	}

	public K floor(K k) {
		Node target = root.floor(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	public K ceiling(K k) {
		Node target = root.ceil(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	public K higher(K k) {
		Node target = root.higher(k);
		if (target == nullNode)
			return null;
		if (belongs(target.key))
			return target.key;
		return null;
	}

	public K pollFirst() {
		K first = first();
		if (first == null)
			throw new NoSuchElementException();
		root.erase(first);
		return first;
	}

	public K pollLast() {
		K last = last();
		if (last == null)
			throw new NoSuchElementException();
		root.erase(last);
		return last;
	}

	public int size() {
		if (from == null && to == null)
			return root.size;
		if (from == null) {
			Node to = toInclusive ? root.floor(this.to) : root.lower(this.to);
			if (to == nullNode)
				return 0;
			return root.indexOf(to) + 1;
		}
		if (to == null) {
			Node from = fromInclusive ? root.ceil(this.from) : root.higher(this.from);
			if (from == nullNode)
				return 0;
			return root.size - root.indexOf(from);
		}
		Node from = fromInclusive ? root.ceil(this.from) : root.higher(this.from);
		if (from == nullNode || !belongs(from.key))
			return 0;
		Node to = toInclusive ? root.floor(this.to) : root.lower(this.to);
		return root.indexOf(to) - root.indexOf(from) + 1;
	}

	public boolean isEmpty() {
		return size() == 0;
	}

	public boolean contains(Object o) {
		return belongs((K) o) && root.search((K) o) != nullNode;
	}

	public Iterator<K> iterator() {
		return new Iterator<K>() {
			private K current = first();

			public boolean hasNext() {
				return current != null;
			}

			public K next() {
				K result = current;
				current = higher(current);
				return result;
			}

			public void remove() {
				TreapSet.this.remove(current);
			}
		};
	}

	public Object[] toArray() {
		Object[] array = new Object[size()];
		int index = 0;
		for (K key : this)
			array[index++] = key;
		return array;
	}

	public <T> T[] toArray(T[] a) {
		if (a.length < size())
			throw new IllegalArgumentException();
		int index = 0;
		for (K key : this)
			a[index++] = (T) key;
		return a;
	}

	public boolean add(K k) {
		if (k == null)
			throw new NullPointerException();
		if (contains(k))
			return false;
		root = root.insert(createNode(k));
		return true;
	}

	protected Node createNode(K k) {
		return new Node(k, rnd.nextLong());
	}

	public boolean remove(Object o) {
		if (!contains(o))
			return false;
		//noinspection unchecked
		root = root.erase((K) o);
		return true;
	}

	public boolean containsAll(Collection<?> c) {
		for (Object o : c) {
			if (!contains(o))
				return false;
		}
		return true;
	}

	public boolean addAll(Collection<? extends K> c) {
		return addAll((Iterable<? extends K>)c);
	}

	public boolean retainAll(Collection<?> c) {
		List<K> toRemove = new ArrayList<K>();
		for (K key : this) {
			if (!c.contains(key))
				toRemove.add(key);
		}
		return removeAll(toRemove);
	}

	public boolean removeAll(Collection<?> c) {
		boolean result = false;
		for (Object o : c)
			result |= remove(o);
		return result;
	}

	public void clear() {
		retainAll(Collections.<Object>emptySet());
	}

	public NavigableSet<K> descendingSet() {
		throw new UnsupportedOperationException();
	}

	public Iterator<K> descendingIterator() {
		return new Iterator<K>() {
			private K current = last();

			public boolean hasNext() {
				return current != null;
			}

			public K next() {
				K result = current;
				current = lower(current);
				return result;
			}

			public void remove() {
				TreapSet.this.remove(current);
			}
		};
	}

	public NavigableSet<K> subSet(K fromElement, boolean fromInclusive, K toElement, boolean toInclusive) {
		return new TreapSet<K>(fromElement, toElement, fromInclusive, toInclusive, comparator, root, nullNode);
	}

	public NavigableSet<K> headSet(K toElement, boolean inclusive) {
		return subSet(null, false, toElement, inclusive);
	}

	public NavigableSet<K> tailSet(K fromElement, boolean inclusive) {
		return subSet(fromElement, inclusive, null, false);
	}

	public Comparator<? super K> comparator() {
		return comparator;
	}

	public SortedSet<K> subSet(K fromElement, K toElement) {
		return subSet(fromElement, true, toElement, false);
	}

	public SortedSet<K> headSet(K toElement) {
		return subSet(null, false, toElement, false);
	}

	public SortedSet<K> tailSet(K fromElement) {
		return tailSet(fromElement, true);
	}

	public K first() {
		if (isEmpty())
			return null;
		if (from == null)
			return root.first().key;
		if (fromInclusive)
			return ceiling(from);
		return higher(from);
	}

	public K last() {
		if (isEmpty())
			return null;
		if (to == null)
			return root.last().key;
		if (toInclusive)
			return floor(to);
		return lower(to);
	}

	public K get(int index) {
		if (index >= size() || index < 0)
			throw new IndexOutOfBoundsException(Integer.toString(index));
		if (from != null)
			index += headSet(from, !fromInclusive).size();
		return root.get(index);
	}

	protected int compare(K first, K second) {
		if (first == null || second == null)
			return -1;
		if (comparator != null)
			return comparator.compare(first, second);
		//noinspection unchecked
		return ((Comparable<? super K>)first).compareTo(second);
	}

	protected class Node {
		protected final K key;
		protected final long priority;
		protected Node left;
		protected Node right;
		protected int size;

		protected Node(K key, long priority) {
			this.key = key;
			this.priority = priority;
			left = nullNode;
			right = nullNode;
			size = 1;
		}

		protected Object[] split(K key) {
			if (compare(key, this.key) < 0) {
				Object[] result = left.split(key);
				left = (Node) result[1];
				result[1] = this;
				updateSize();
				return result;
			}
			Object[] result = right.split(key);
			right = (Node) result[0];
			result[0] = this;
			updateSize();
			return result;
		}

		protected void updateSize() {
			size = left.size + right.size + 1;
		}

		protected Node insert(Node node) {
			if (node.priority > priority) {
				Object[] result = split(node.key);
				node.left = (Node) result[0];
				node.right = (Node) result[1];
				node.updateSize();
				return node;
			}
			if (compare(node.key, this.key) < 0) {
				left = left.insert(node);
				updateSize();
				return this;
			}
			right = right.insert(node);
			updateSize();
			return this;
		}

		protected Node merge(Node left, Node right) {
			if (left == nullNode)
				return right;
			if (right == nullNode)
				return left;
			if (left.priority > right.priority) {
				left.right = left.right.merge(left.right, right);
				left.updateSize();
				return left;
			}
			right.left = right.left.merge(left, right.left);
			right.updateSize();
			return right;
		}

		protected Node erase(K key) {
			int value = compare(key, this.key);
			if (value == 0)
				return merge(left, right);
			if (value < 0) {
				left = left.erase(key);
				updateSize();
				return this;
			}
			right = right.erase(key);
			updateSize();
			return this;
		}

		protected Node lower(K key) {
			if (compare(key, this.key) <= 0)
				return left.lower(key);
			Node result = right.lower(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node floor(K key) {
			if (compare(key, this.key) < 0)
				return left.floor(key);
			Node result = right.floor(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node higher(K key) {
			if (compare(key, this.key) >= 0)
				return right.higher(key);
			Node result = left.higher(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node ceil(K key) {
			if (compare(key, this.key) > 0)
				return right.ceil(key);
			Node result = left.ceil(key);
			if (result == nullNode)
				return this;
			return result;
		}

		protected Node first() {
			if (left == nullNode)
				return this;
			return left.first();
		}

		protected Node last() {
			if (right == nullNode)
				return this;
			return right.last();
		}

		protected Node search(K key) {
			int value = compare(key, this.key);
			if (value == 0)
				return this;
			if (value < 0)
				return left.search(key);
			return right.search(key);
		}

		public int indexOf(Node node) {
			if (this == node)
				return left.size;
			if (compare(node.key, this.key) > 0)
				return left.size + 1 + right.indexOf(node);
			return left.indexOf(node);
		}

		public K get(int index) {
			if (index < left.size)
				return left.get(index);
			else if (index == left.size)
				return key;
			else
				return right.get(index - left.size - 1);
		}
	}

	private class NullNode extends Node {
		private NullNode() {
			super(null, Long.MIN_VALUE);
			left = this;
			right = this;
			size = 0;
		}

		protected Object[] split(K key) {
			return new Object[]{this, this};
		}

		protected Node insert(Node node) {
			return node;
		}

		protected Node erase(K key) {
			return this;
		}

		protected Node lower(K key) {
			return this;
		}

		protected Node floor(K key) {
			return this;
		}

		protected Node higher(K key) {
			return this;
		}

		protected Node ceil(K key) {
			return this;
		}

		protected Node first() {
			throw new NoSuchElementException();
		}

		protected Node last() {
			throw new NoSuchElementException();
		}

		protected void updateSize() {
		}

		protected Node search(K key) {
			return this;
		}


	}
}

