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
# coding: utf-8
# Your code here!

try:
   while True:
      n, k = map(int, input().split())
      if n + k == 0:
         break
      
      l = []
      for i in range(n):
         l.append(int(input()))

      s1 = 0
      for i in range(k):
         s1 += l[i]
      
      ma = 0
      s2 = 0
      for j in range(n - k):
         s2 = s1 - l[j] + l[j + k]
         if s2 > ma:
            ma = s2
         s1 = s2
      print(ma)

except EOFError:
   pass


