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 <cstdio>
#include <vector>
#include <algorithm>
using namespace std;


int main()
{
while(true) {
int n, k;
vector<int> x;
scanf("%d%d", &n, &k);
if(n == 0)
break;
x.resize(n);
for(int i = 0; i < n; ++i)
scanf("%d", &x[i]);
int cur = 0, ans;
for(int i = 0; i < k; ++i)
cur += x[i];
ans = cur;
for(int i = k; i < n; ++i) {
cur += x[i];
cur -= x[i - k];
ans = max(ans, cur);
}
printf("%d\n", ans);
}
return 0;
}