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>
#include <string>
#include <algorithm>
using namespace std;

int main(){
  int i,j,n,k,a[100000],b[100000],s,max;
  while(1){
    cin >> n >> k;
    if(n == 0 && k == 0) break;
    max = 0;
    s = 0;
    for(i=0;i<n;i++){
      cin >> a[i];

      s += a[i];
      b[i] = a[i];
      if(i >= k-1){
	if(max < s) max = s;
	s -= b[i-(k-1)];
      }
    }
    cout << max << endl;
  }
  return 0;
}