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 <bits/stdc++.h>
using namespace std;

#define loop(i,n) for(int i=1;i<=n;i++)
int a[100002];
int s[100002];

int main(){
  while(1){
    int n,k;
    cin>>n>>k;
    if(n==0)return 0;
    loop(i,n)cin>>a[i];
    s[1]=0;
    loop(j,k){
      s[1]+=a[j];
    }
    int m=s[1];
    loop(i,n-k+1){
      if(i==1)continue;
      s[i]=s[i-1]-a[i-1]+a[i+k-1];
      m=max(m,s[i]);
    }
    cout<<m<<endl;
  }
  return 0;
}