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<cstdio>
#include<iostream>
using namespace std;
int main(){
  int n,k;
  cin >> n >> k;
  while(n!=0|k!=0){
    int max=0,ans,i;
    int a[n];
    for(i = 0;i < n;i++){
      scanf("%d",&a[i]);
      if(i < k){
	max += a[i];
	ans = max;
      }
      else {
	max = max + (a[i] - a[i-k]);
	if(ans < max) ans = max;
      }
    }
    printf("%d\n",ans);
    cin >> n >> k;
  }
  return (0);
}