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
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int cnt = -9;
        int range = -9;
        String line;
        List<Integer> inputs = new ArrayList<>();
        while ((line = br.readLine().trim()) != null && !line.isEmpty() && !"0 0".equals(line)) {
            if(cnt < 0) {
                List<Integer> list = Arrays.stream(line.split(" ")).map(Integer::valueOf).collect(Collectors.toList());
                cnt = list.get(0);
                range = list.get(1);
            } else {
                inputs.add(Integer.valueOf(line));
                if(--cnt==0) {
                    output(inputs, range);
                    inputs.clear();
                    cnt = -9;
                }
            }
        }
    }

    public static void output(List<Integer> list, int range) {
        int sum = IntStream.range(0,range).map(j->list.get(j)).sum();
        int max = sum;
        for(int i=range; i<list.size(); i++) {
            sum = sum - list.get(i-range) + list.get(i);
            if(max<sum) max=sum;
        }
        System.out.println(max);
    }
}