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<cstdio>

using namespace std;

int main(void)
{
int n,k,s,b;
while(1)
{
cin >> n >>k;
if(n==0 && k==0)
break;
int m[100001]={0};
int a[100001];

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

m[0]=0;
for(int i=0;i<n;i++)
m[i+1]=m[i]+a[i];

s=0;

for(int i=1;i+k<=n;i++)
{
b=m[i+k]-m[i];
if(s<b)
s=b;
}
cout << s << endl;
}
return 0;
}
