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<stdio.h>

using namespace std;


int main(){

while(1){
    int n, k;
    cin>> n>> k;
    if(n==0&&k==0) break;
    int a[n];
    for(int i=0; i<n; i++){
        cin>> a[i];
    }
    int s[n+1];
    fill(s, s+n+1, 0);
    for(int i=0; i<n; i++){
        s[i+1]=s[i]+a[i];
    }
    int ans=-100100100;
    for(int i=k; i<=n; i++){
        ans=max(ans, s[i]-s[i-k]);
    }

    cout<< ans<< endl;
}
    return 0;
}