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
#!/usr/bin/env python3

import sys

sys.setrecursionlimit(10**7)


def read_h(typ=int):
    return list(map(typ, input().split()))


def read_v(n, m=1, typ=int):
    return [read_h(typ) if m > 1 else typ(input()) for _ in range(n)]


def solve():
    n, k = read_h()
    arr = read_v(n)

    cumul = [sum(arr[:i]) for i in range(len(arr) + 1)]
    #  print(cumul)

    ans = 0
    for i in range(n - k + 1):
        s = cumul[i + k] - cumul[i]
        ans = max(ans, s)

    print(ans)


def main():
    while True:
        n, k = read_h()
        if (n, k) == (0, 0):
            break

        arr = read_v(n)

        cumul = [0]
        for i in range(n):
            cumul.append(cumul[i] + arr[i])

        ans = 0
        for i in range(n - k + 1):
            s = cumul[i + k] - cumul[i]
            ans = max(ans, s)

        print(ans)


if __name__ == '__main__':
    main()

