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<cstdio>
#include<math.h>
#include<algorithm>

using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
const int INF=1001001001;
int N,K;
int A[100002];


int main(){
	while(1){
	scanf("%d %d",&N,&K);
	if(N==0&&K==0)break;
	rep(i,N)scanf("%d",&A[i]);
	long long int ans=0;
	long long int sans=0;
	rep(i,K)sans+=A[i];
	ans=sans;
	rep(i,N-K){
		sans-=A[i];
		sans+=A[i+K];
		ans=max(ans,sans);
	}
	printf("%lld\n",ans);
	}
}