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>
#include <string>
using namespace std;
int main(){
int n;
int k;
int b;
int c;//現在の和
int d;//最高値
while(cin>>n){
if(n==0){break;}
cin>>k;
int a[n];
b=0;
while(b<n){
cin >>a[b];
b=b+1;}
c=0;
b=0;
while(b<k){
c=c+a[b];
b=b+1;}
d=c;
while(b<n){
c=c-a[b-k]+a[b];
if(c>d){d=c;}
b=b+1;}
cout << d<<endl;}
}