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
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")

# https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/all/DSL_1_B
import sys
sys.setrecursionlimit(1000000)
INF = float("inf")

while True:
    N,K = map(int,sys.stdin.readline().split())
    if N==0 and K==0:
        exit()
    a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param

    com = [0]*(N+1)
    for i in range(N):
        com[i+1]=com[i]+a[i]

    ret = -INF
    for i in range(N-K):
        ret = max(ret,com[i+K]-com[i])
    print(ret)
