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>
using namespace std;

int main() {
  int n, k;
  while(cin >> n >> k, n+k) {
    vector<int> a(n);
    for(int i = 0; i < n; i++) cin >> a[i];

    long long ans = -10000000000;
    for(int i = 0; i < n-k; i++) {
      long long sum = 0;
      for(int j = 0; j < k; j++) {
	sum += a[i+j];
      }
      if(ans < sum) ans = sum;
    }
    cout << ans << endl;
  }
}