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
#include <algorithm>
#include <cstdio>
typedef long long ll;
ll dp[100000];
int v[100000];
int main()
{
    int n, k;
    while (scanf("%d%d", &n, &k), n|k) {
        for (int i=0; i<n; ++i) scanf("%d", v+i);
        dp[k-1] = 0;
        for (int i=0; i<k; ++i) dp[k-1] += v[i];
        for (int i=k; i<n; ++i) dp[i] = dp[i-1] - v[i-k] + v[i];
        printf("%lld\n", *std::max_element(dp+k-1, dp+n));
    }
    return 0;
}