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;
bool solve(){
    int arr[100001]={0};
    int N,K;
    scanf("%d%d",&N,&K);
    if(N==0&&K==0)return false;
    for(int i=0;i<N;i++){
        scanf("%d",&arr[i+1]);
        arr[i+1]+=arr[i];
    }
    int ma=INT_MIN;
    for(int i=0;i+K<=N;i++){
        ma=max(ma,arr[i+K]-arr[i]);
    }
    printf("%d\n",ma);
    return true;
}

int main(){
    while(solve());
}