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
def mips():
    return map(int,input().split())
def ii():
    return int(input())
#AOJ_maximum sum
def procedure():
    N,K = mips()
    if N == 0:
        sys.exit(0)
    A = []
    res = -(10**100)
    for _ in range(N):
        a = ii()
        A.append(a)
    S = [0]
    for i in range(N):
        s = S[i] + A[i]
        S.append(s)
    for i in range(N-K):
        res = max(res,S[i+K]-S[i])
    print(res)
while True:
    procedure()
