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 <algorithm>
using namespace std;
typedef long long int ll;
int main(){
	int n,k;
	while(1){
		scanf("%d %d",&n,&k);
		if(n==0)	return 0;
		int a[n];
		for(int i=0;i<n;i++)	scanf("%d",&a[i]);
		ll bgs=0,temp=0;
		for(int i=0;i<k;i++)	temp+=a[i];
		bgs=temp;
		for(int i=1;i<=n-k;i++){
			temp=temp-a[i-1]+a[i+k-1];
			bgs=max(bgs,temp);
		}
		printf("%lld\n",bgs);
	}
}