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
public class Main{
  public void run(java.io.InputStream in, java.io.PrintStream out){
    java.util.Scanner sc = new java.util.Scanner(in);
    int n, k, i, j, max, sum;
    int[] a;
    for(;;out.println(max)){
      n = sc.nextInt(); k = sc.nextInt();
      if(n == 0 && k == 0)break;
      max = -k * 10001;
      a = new int[n];
      for(i = 0;i < n;i++)a[i] = sc.nextInt();
      sum = 0;
      for(i = 0;i < k;i++)sum += a[i];
      max = sum;
      for(i = 0;i < n - k;i++){
        sum += (a[i + k] - a[i]);
        if(max < sum)max = sum;
      }
    }

    sc.close();
  }
  public static void main(String[] args){
    (new Main()).run(System.in, System.out);
  }
}