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;
cin >> n >> k;
while(n!=0||k!=0){
  int i=0, a[n], S[n-1];
  S[0] = 0;
  while(i < n){
    cin >> a[i];
    if (i>=1)
      S[i] = S[i-1]+a[i-1];
    i++;
  }
  i = 0;
  int m = S[k]-S[0];
  while(k+i<n){
    if (m < S[i+k]-S[i])
      m = S[i+k]-S[i];
    i++;
  }
  cout << m << endl;
cin >> n >> k;
}}


