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 <stdio.h>
int RB[100005],ans;
int main() {int N,K,i,j;while (1) {scanf("%d %d",&N,&K);if (!N || N==EOF) return 0;ans=-1000000007,j=0;for (i=0,K--;i<K;i++) scanf("%d",&RB[i]),j+=RB[i];for (i=K;i<N;i++) scanf("%d",&RB[i]),j+=RB[i],(ans=(ans>j)?ans:j),j-=RB[i-K]; printf("%d\n",ans);}}