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<stdio.h>
#include<iostream>
using namespace std;

int main(){
    int n,a[100001]={0},k,sum,p;
int i,j,h;
while(1){
cin>>n>>k;
if(n==0&&k==0)break;
cin>>a[1];
for(i=2;i<=n;i++){
	cin>>a[i];
	a[i]+=a[i-1];
}
sum=a[k];
for(i=k+1;i<=n;i++){
    sum=max(sum,a[i]-a[i-k]);
	}
cout<<sum<<endl;
}
return 0;
}

