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 <bits/stdc++.h>
using namespace std;

int main()
{
int n,k,d,S ;
while(1){ 
cin >> n >> k ;
if(n==0&&k==0){
break;
}
vector<int> a(n) ;
for(int i=0;i<n;i++){
cin >> d ;
a.at(i)=d ;
}
S=0 ;
for(int j=0;j<k;j++){
S=S+a.at(j) ;
}
int A=0;
A=S ;
for(int l=0;l<n-k;l++){
S=S-a.at(l)+a.at(l+k);
A=max(A,S) ;
}
cout << A << endl;
}
}

