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>

using namespace std;

#define MAX 100000

int main(){

	int n,k,a[MAX];
	long long num,max;

	while(1){

		cin>>n>>k;
		if(n==0&&k==0) break;

		for(int i=0;i<n;i++){
			cin>>a[i];
		}

		num=0;
		for(int j=0;j<k;j++){
			num+=a[j];
		}
		max=num;

		for(int i=0;i<n-k;i++){
			num-=a[i];
			num+=a[i+k];
			max=(max<num)?num:max;
		}
		
		cout<<max<<endl;
		
	}

	return 0;
}