problem

Given a sequence of n integers a1, a2, ..., an and a positive integer k (1 ≤ k ≤ n), then the sum of k consecutive integers Si = ai + ai + Create a program that outputs the maximum value of 1 + ... + ai + k-1 (1 ≤ i ≤ n --k + 1).



input

The input consists of multiple datasets. Each dataset is given in the following format. The input ends on a line containing two zeros.

On the first line, the positive integer n (1 ≤ n ≤ 100000) and the positive integer k (1 ≤ k ≤ n) are written in this order, separated by blanks. The first + i lines after the second line. (1 ≤ i ≤ n) contains the i-th term ai (-10000 ≤ ai ≤ 10000) in the sequence. Of the scoring data, 60% of the points are n ≤ 5000, k ≤ 1000. Meet.

The number of datasets does not exceed 5.

output

The maximum value of Si is output to one line for each data set.

Examples

Input

5 3
2
5
-4
10
3
0 0


Output

11


Input

None


Output

None
#include <iostream>
using namespace std;
int main()
{
  int n,k;
  for(;cin>>n>>k,n;)
    {
      int d[n];
      for(int i=0;i<n;i++)
	cin>>d[i];
      int sum=0;
      int i;
      for(i=0;i<k;i++)
	{
	  sum+=d[i];
	}
      int max=sum;
      for(;i<n;i++)
	{
	  sum+=d[i];
	  sum-=d[i-k];
	  if(max<sum)
	    max=sum;
	}

      cout<<max<<endl;
    }
}