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
import sys
input=sys.stdin.readline

def shak(n,k):

	a=[int(input()) for _ in range(n)]


	l,r=0,k
	res=0
	cnt=sum(a[l:r])
	while r<n:
		res=max(res,cnt)

		cnt=cnt+a[r]-a[l]
		r+=1
		l+=1
	print(res)

for i in range(5):
	n,k=map(int,input().split())
	if n==k==0:exit()
	shak(n,k)
