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>
#define loop(times) for(int i=0;i<(times);i++)

using namespace std;

int main() {
    while(1<2){
    int n,K;
    long long max;
    cin>>n>>K;
    if(n==0&&K==0)break;
    int S[n];
    int a[n];
    S[0]=0;
    loop(n) cin>>a[i];
    loop(K) S[0]+=a[i];
    max=S[0];
        
    for(int j=1;j<n-K+1;j++){
    S[j]=S[j-1]+a[j+K-1]-a[j-1];
    if(max<=S[j])max=S[j];
    }
        
    cout<<max<<endl;
    }
}
