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;

#define INT_MIN -2147483648
#define MAX_N 100010
int N, K;
int S[MAX_N];

int main() {
  while (true) {
  cin >> N >> K;
  if (N == 0 && K == 0) break;
  for (int i=0; i<N; i++) cin >> S[i];

  int pre = 0;
  for (int i=0; i<K; i++) pre += S[i];
  int ans = pre;

  for (int i=1; i<=N-K; i++) {
    pre = pre - S[i-1] + S[i+K-1];
    ans = max(ans, pre);
  }
  cout << ans << "\n";
  }
  return 0;
}