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
def func(n,k):
    SUM = 0
    ans = 0
    A = [int(input()) for _ in range(n)]
    for i in range(k):
        SUM += A[i]
    for i in range(k,len(A)):
        ans = max(ans,SUM+A[i]-A[i-k])
        SUM = SUM+A[i]-A[i-k]
    print(ans)

for _ in range(10):
    n,k = [int(s) for s in input().split()]
    if n == 0 and k ==0:
        break
    else:
        func(n,k)
