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
# -*- coding: utf-8 -*-
"""
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0516

"""
import sys
from sys import stdin
from collections import deque
input = stdin.readline


def main(args):
    while True:
        n, k = map(int, input().split())
        if n == 0 and k == 0:
            break

        d = deque([int(input()) for _ in range(k)])
        sum_value = sum(d)
        maximum_sum = sum_value

        for _ in range(n-k):
            v = int(input())
            o = d.popleft()
            sum_value = sum_value - o + v
            if sum_value > maximum_sum:
                maximum_sum = sum_value
            d.append(v)

        print(maximum_sum)


if __name__ == '__main__':
    main(sys.argv[1:])
    