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 <algorithm>
#define INF 90000000000
using namespace std;

int ary[100010];
int main(){
	int N,K;
	long long cnt,ccnt;
	while(1){
		cin>>N>>K;
		if(N==0&&K==0) break;
		for(int i=1;i<=N;i++){
			cin>>ary[i];
		}
		ccnt=0;
		for(int j=1;j<=K;j++){
			ccnt+=ary[j];
		}
		cnt=ccnt;
		for(int i=2;i+(K-1)<=N;i++){
			ccnt+=ary[i+(K-1)];
			ccnt-=ary[i-1];
			cnt=max(cnt,ccnt);
		}
		cout<<cnt<<endl;
	}
	return 0;
}