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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

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

		while(true){
			String[] tmpArray = br.readLine().split(" ");

			int n = Integer.parseInt(tmpArray[0]);
			int k = Integer.parseInt(tmpArray[1]);
			
			if(n == 0 && k == 0){
				break;
			}
			
			int[] input = new int[n];
			for(int i = 0; i < n; i++){
				input[i] = Integer.parseInt(br.readLine());
			}
			
			int sum = 0;
			int max = Integer.MIN_VALUE;
			//????????????????????????????¨???????????????????
			for(int i = 0; i < k; i ++){
				sum += input[i];
			}
			max = sum;
			//System.out.println("sum "+sum);
			
			for(int i = 1; i <= n - k; i++){
				sum += input[i + k - 1];
				sum -= input[i - 1];
				
				//System.out.println("sum "+sum);
				if(sum > max){
					max = sum;
				}
			}
			
			System.out.println(max);
			
		}
	}

}