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
from itertools import accumulate
# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline


def solve():
    N, K = map(int, input().split())
    if N == 0:
        exit()
    A = [int(input()) for _ in range(N)]
    S = sum(A[:K])

    ans = S
    for i in range(K, N):
        S = S-A[i-K]+A[i]
        ans = max(ans, S)
    print(ans)


def solve2():
    N, K = map(int, input().split())
    if N == 0:
        exit()
    else:
        A = [int(input()) for _ in range(N)]
        A = [0]+list(accumulate(A))
        ans = max([A[i+K]-A[i] for i in range(N-K)])
        print(ans)


while True:
    solve2()

