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>
using namespace std;
int a[100010];
long long ans,maxx;
int main()
{
	int i,n,m;
	while(cin>>n>>m&&n!=0&&m!=0)
	{
		ans=-9999999,maxx=0;
		for(i=1;i<=n;i++)
		{
			cin>>a[i];
			if(i<m)maxx+=a[i];
			else if(i>=m)
			{ 
			    maxx+=a[i];
			    if(maxx>ans)ans=maxx;
			    maxx-=a[i-m+1];
			}
		}
		cout<<ans<<endl;
	}
	return 0;
}
