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.util.Scanner;


public class Main {

		public static class BIT{
				int[] dat;
				
				public BIT(int n){
						dat = new int[n + 1];
				}
				
				public void add(int k, int a){
						for(int i = k + 1; i < dat.length; i += i & -i){
								dat[i] += a;	
						}
				}
				
				public int sum(int s, int t){
						if(s > 0) return sum(0, t) - sum(0, s);
						
						int ret = 0;
						for(int i = t; i > 0; i -= i & -i) {
								ret += dat[i];
						}
						return ret;
				}
				
				public int get(int k){
						int p = Integer.highestOneBit(dat.length - 1);
						for(int q = p; q > 0; q >>= 1, p |= q){
								if( p >= dat.length || k < dat[p]) p ^= q;
								else k -= dat[p];
						}
						return p;
				}
		}
		
		public static void main(String[] args){
				Scanner sc = new Scanner(System.in);
				
				while(true){
						final int n = sc.nextInt();
						final int k = sc.nextInt();

						if(n == 0 && k == 0){
								break;
						}

						BIT bit = new BIT(n);
						for(int i = 0; i < n; i++){
								bit.add(i, sc.nextInt());
						}

						int max = Integer.MIN_VALUE;
						for(int start = 0; start < n - k + 1; start++){
								max = Math.max(max, bit.sum(start, start + k));
								//System.out.println("[" + start + " " + (start + k) + ") = " + bit.sum(start, start + k));
						}
						
						System.out.println(max);
				}
		}
}