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 <iostream>
using namespace std;

int main(){
	while(1){
		long n, k;
		long s[100001]; //i番目までの和
		s[0]=0;
		
		scanf(" %ld %ld", &n, &k);
		if(n==0) break;
		for(long i=0; i<n; ++i){
			int a;
			scanf(" %d", &a);
			s[i+1] = s[i]+a;
		}
		
		long max=-1500000000;
		for(int i=1; i+k<=n; ++i){
			long tmp=s[i+k]-s[i];	
			if(tmp>max) max=tmp;
		}
		
		printf("%ld\n", max);
	}
}