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>
#include<vector>

int main(){
  int n,k;
  long long int ans=-1000000000;
while(true){
  std::cin>>n>>k;
if(n==0&&k==0)break;
  std::vector<long long int>vec(n+1,0);
  long long int sub;
  for(int i=1;i<=n;i++){
    std::cin>>sub;
    vec.at(i)=vec.at(i-1)+sub;
  }
  for(int i=n;i>=k;i--){
    ans=std::max(vec.at(i)-vec.at(i-k),ans);
  }
  std::cout<<ans<<std::endl;
}
  return 0;
}

