This morning, Roman woke up and opened the browser with n opened tabs numbered from 1 to n. There are two kinds of tabs: those with the information required for the test and those with social network sites. Roman decided that there are too many tabs open so he wants to close some of them.

He decided to accomplish this by closing every k-th (2 ≤ k ≤ n - 1) tab. Only then he will decide whether he wants to study for the test or to chat on the social networks. Formally, Roman will choose one tab (let its number be b) and then close all tabs with numbers c = b + i ⋅ k that satisfy the following condition: 1 ≤ c ≤ n and i is an integer (it may be positive, negative or zero).

For example, if k = 3, n = 14 and Roman chooses b = 8, then he will close tabs with numbers 2, 5, 8, 11 and 14.

After closing the tabs Roman will calculate the amount of remaining tabs with the information for the test (let's denote it e) and the amount of remaining social network tabs (s). Help Roman to calculate the maximal absolute value of the difference of those values |e - s| so that it would be easy to decide what to do next.

Input

The first line contains two integers n and k (2 ≤ k < n ≤ 100) — the amount of tabs opened currently and the distance between the tabs closed.

The second line consists of n integers, each of them equal either to 1 or to -1. The i-th integer denotes the type of the i-th tab: if it is equal to 1, this tab contains information for the test, and if it is equal to -1, it's a social network tab.

Output

Output a single integer — the maximum absolute difference between the amounts of remaining tabs of different types |e - s|.

Examples

Input


4 2
1 1 -1 1


Output


2


Input


14 3
-1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1


Output


9

Note

In the first example we can choose b = 1 or b = 3. We will delete then one tab of each type and the remaining tabs are then all contain test information. Thus, e = 2 and s = 0 and |e - s| = 2.

In the second example, on the contrary, we can leave opened only tabs that have social networks opened in them.
import java.util.*;
import java.io.*;
import java.lang.reflect.Array;

		public class codeforces
		{	
			public static void main(String[] args)
			{
				InputReader in = new InputReader(System.in);
				PrintWriter pw = new PrintWriter(System.out);

				int n = in.nextInt();
				int k = in.nextInt();
				int[] a = new int[n];
				int sum = 0, ans = 0, max = 0;
				
				for(int i=0;i<n;i++)
				{
					a[i] = in.nextInt();
					sum += a[i];
				}
				
				for(int i=0;i<k;i++)
				{
					ans = sum;
					for(int j=i;j<n;j+=k)
					{
						ans -= a[j];
					}
					
					if(ans < 0)
						ans = -ans;
					
					max = Math.max(max, ans);
				}
				
				pw.println(max);
				
				pw.flush();
				pw.close();
			}
			
		/*	public static void DFS(int sourse)
			{
				int count = 0;
				visited[sourse] = true;
				
				for(int u : adj[sourse])
				{
					if(!visited[u])
					{
						DFS(u);
					}
				}
				
				
			}*/
			
			public static ArrayList Divisors(long n)
			{
			    ArrayList<Long> div = new ArrayList<>();
			    
			    for (long i=1; i<=Math.sqrt(n); i++)
			    {
			        if (n%i == 0)
			        {
			        	div.add(i);
			                
			            if(n/i != i)
			            	div.add(n/i);
			        }
			    }
			    return div;
			}
		
			public static int BinarySearch(long[] a, long k)
			{
				int n = a.length;
				int i = 0, j = n-1;
				int mid = 0;
				
				if(k < a[0])
					return 0;
				else if(k >= a[n-1])
					return n;
				else
				{
					while(j - i > 1)
					{
						mid = (i+j)/2;
						
						if(k >= a[mid])
							i = mid;
						else
							j = mid;
					}
				}
				
				return i+1;
			}
			public static long GCD(long a,long b)
			{
				if(b==0)
					return a;
				else
					return GCD(b,a%b);
			}
			
			public static long LCM(long a,long b)
			{
				return (a*b)/GCD(a, b);
			}
			
			static class pair implements Comparable<pair>
			{
				Integer x, y;
				pair(int x,int y)
				{
					this.x=x;
					this.y=y;
				}
				
				public int compareTo(pair o) {
					int result = x.compareTo(o.x);
					if(result==0)
						result = y.compareTo(o.y);
					
					return result;
				}  
				
				public String toString()
				{
					return x+" "+y;
				}
				
				public boolean equals(Object o)
				{
					if (o instanceof pair)
				    {
						pair p = (pair)o;
						return p.x - x == 0 && p.y - y == 0 ;
					}
					return false;
				}
				
				public int hashCode()
				{
					return new Long(x).hashCode()*31 + new Long(y).hashCode();
				}
			}
			
			static class InputReader 
			{
				 
				private final InputStream stream;
				private final byte[] buf = new byte[8192];
				private int curChar, snumChars;
				private SpaceCharFilter filter;
		 
				public InputReader(InputStream stream) 
				{
					this.stream = stream;
				}
		 
				public int snext() 
				{
					if (snumChars == -1)
						throw new InputMismatchException();
					if (curChar >= snumChars) 
					{
						curChar = 0;
						try 
						{
							snumChars = stream.read(buf);
						} 
						catch (IOException e) 
						{
							throw new InputMismatchException();
						}
						if (snumChars <= 0)
							return -1;
					}
					return buf[curChar++];
				}
		 
				public int nextInt() 
			    {
					int c = snext();
					while (isSpaceChar(c)) 
					{
						c = snext();
					}
					int sgn = 1;
					if (c == '-')
				    {
						sgn = -1;
						c = snext();
					}
					int res = 0;
					do 
					{
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = snext();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
		 
				public long nextLong()
			    {
					int c = snext();
					while (isSpaceChar(c)) 
					{
						c = snext();
					}
					int sgn = 1;
					if (c == '-') 
					{
						sgn = -1;
						c = snext();
					}
					long res = 0;
					do 
					{
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = snext();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
		 
				public int[] nextIntArray(int n) 
				{
					int a[] = new int[n];
					for (int i = 0; i < n; i++) 
					{
						a[i] = nextInt();
					}
					return a;
				}
		 
				public String readString()
			    {
					int c = snext();
					while (isSpaceChar(c)) 
					{
						c = snext();
					}
					StringBuilder res = new StringBuilder();
					do 
					{
						res.appendCodePoint(c);
						c = snext();
					} while (!isSpaceChar(c));
					return res.toString();
				}
		 
				public String nextLine() 
				{
					int c = snext();
					while (isSpaceChar(c))
						c = snext();
					StringBuilder res = new StringBuilder();
					do 
					{
						res.appendCodePoint(c);
						c = snext();
					} while (!isEndOfLine(c));
					return res.toString();
				}
		 
				public boolean isSpaceChar(int c) 
				{
					if (filter != null)
						return filter.isSpaceChar(c);
					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				}
		 
				private boolean isEndOfLine(int c) 
				{
					return c == '\n' || c == '\r' || c == -1;
				}
		 
				public interface SpaceCharFilter
			    {
					public boolean isSpaceChar(int ch);
				}
			}
			
			static class CodeX {
	        public static void sort(long arr[]) {
	            merge_sort(arr, 0, arr.length - 1);
	        }
	
	        private static void merge_sort(long A[], long start, long end) {
	            if (start < end) {
	                long mid = (start + end) / 2;
	                merge_sort(A, start, mid);
	                merge_sort(A, mid + 1, end);
	                merge(A, start, mid, end);
	            }
	
	        }
	
	        private static void merge(long A[], long start,long mid, long end) {
	            long p = start, q = mid + 1;
	            long Arr[] = new long[(int)(end - start + 1)];
	            long k = 0;
	
	            for (int i = (int)start; i <= end; i++) {
	                if (p > mid)
	                    Arr[(int)k++] = A[(int)q++];
	
	                else if (q > end)
	                    Arr[(int)k++] = A[(int)p++];
	
	                else if (A[(int)p] < A[(int)q])
	                    Arr[(int)k++] = A[(int)p++];
	
	                else
	                    Arr[(int)k++] = A[(int)q++];
	            }
	            for (int i = 0; i < k; i++) {
	                A[(int)start++] = Arr[i];
	            }
	
	        }
	
	    }
		}	
		

			