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;
  int a[100001];

  int max;
  int sum_seq;


  while(cin >> n >> k) {

    if(n==0 && k==0) break;

    for(int i=0;i<n;i++) cin >> a[i];

    max=0;

    sum_seq=0;

    for(int i=0;i<k;i++) sum_seq+=a[i];

    for(int i=0;i<=n-k;i++) {

      if(max<sum_seq) max=sum_seq;

      if(i!=n-k) sum_seq+=a[i+k]-a[i];

    }

    cout << max << endl;

  }

  return 0;

}