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 <iostream>
#include <algorithm>
using namespace std;

int a[100001],b[100001];

int f(int i,int j){
	return b[i] - b[j+1];
}

int main(){
	int n,k;
	while( cin >> n >> k , n||k ){
		b[0] = 0;
		for(int i=0 ; i < n ; i++ ){
			cin >> a[i];
			b[0] += a[i];
		}
		for(int i=1 ; i <= n ; i++ ){
			b[i] = b[i-1] - a[i-1];
		}
		int s = f(0,k-1);
		for(int i=1 ; i+k < n ; i++ ){
			s = max( s , f(i,i+k-1) );
		}
		cout << s << endl;
	}
}