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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
const int INF = (1 << 29);

int main()
{
  while (1)
  {
    int n, k;
    cin >> n >> k;
    if (n == 0 && k == 0)
      break;
    int a[n];
    rep(i, n) cin >> a[i];
    int s[n + 1];
    s[0] = 0;
    rep(i, n + 1) s[i + 1] = s[i] + a[i];
    int ans = -INF;
    rep(i, n - k) ans = max(ans, s[i + k] - s[i]);
    cout << ans << endl;
  }
}
