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>
#include<algorithm>
using namespace std;
long long m[100000][2];
int main(){
while(1){
long long n,k,i,j,x=0;
cin>>n>>k;
if(n==0&&k==0)break;
for(i=0;i<n;i++)cin>>m[i][0];
m[0][1]=m[0][0];
for(i=1;i<n;i++){
m[i][1]=m[i-1][1]+m[i][0];
}
x=m[k-1][1];
for(i=k;i<n;i++){
x=max(x,m[i][1]-m[i-k][1]);
}
cout<<x<<endl;
}
return 0;
}