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, permutations, combinations, combinations_with_replacement, groupby, product
# import math
# import numpy as np  # Pythonのみ！
# from operator import xor
# import re
# from scipy.sparse.csgraph import connected_components  # Pythonのみ！
# ↑cf.  https://note.nkmk.me/python-scipy-connected-components/
# from scipy.sparse import csr_matrix
# import string
import sys

sys.setrecursionlimit(10 ** 5 + 10)


def input(): return sys.stdin.readline().strip()


def resolve():
    while True:
        n, m = map(int, input().split())
        if [n, m] == [0, 0]:
            break
        else:
            A = [int(input()) for i in range(n)]
            B = [0] + A
            # 累積和を格納したリスト．A[l:r]の総和はB[r] - B[l]
            B = list(accumulate(B))

            val = max([B[i + m] - B[i] for i in range(n - m + 1)])
            print(val)

resolve()
