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<cstdio>
#include<string>
#include<vector>
#include<algorithm>
using namespace std;
typedef long long int ll;

int main()
{
    int n,m,a[100000];
for(;;){
cin >> n >> m;
if(n==0&&m==0)return 0;
for(int i=0;i<n;i++)cin >> a[i];
int ans=0;
int x=0;
for(int i=0;i<m;i++)x+=a[i];
ans=max(ans,x);
for(int i=0;i<n-m;i++){
x+=a[i+m];
x-=a[i];
ans=max(ans,x);
}
printf("%d\n",ans);
}
}