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
# AOJ 0516: Maximum Sum
# Python3 2018.6.30 bal4u

a, s = [0]*100003, [0]*100003
while True:
	n, k = map(int, input().split())
	if n == 0: break
	s[0] = a[0] = int(input())
	for i in range(1, n):
		a[i] = int(input())
		s[i] = s[i-1] + a[i]
		if i >= k: s[i] -= a[i-k]
	ans = s[k-1]
	for i in range(k, n):
		if s[i] > ans: ans = s[i]
	print(ans)
