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>
#define REP(i, a, n) for(int i = a; i < n; i++)
using namespace std;


int n, k;
int a[100000];
int s, m;

int main(void) {
  while(cin >> n >> k, !(n == 0 && k == 0)) {
    REP(i, 0, n) {
      cin >> a[i];
    }

    s = 0;
    REP(i, 0, k) {
      s += a[i];
    }

    m = s;
    REP(i, k, n) {
      s += a[i] - a[i - k];
      if(s > m) m = s;
    }

    cout << m << endl;
  }

  return 0;
}