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<limits.h>

#define N 100000
int n, k;
int a[N];

int input(){
	int i;
	std::cin >> n >> k;
	for( i = 0; i < n; i++ ){ std::cin >> a[i]; }
	return n;
}

int func(){
	int sum = 0, m = 0, i;
	for( i = 0; i < k; i++ ){ sum += a[i]; }
	m = sum;
	for( i = k; i < n; i++ ){
		sum += a[i] - a[i-k];
		m = (sum>m?sum:m);
	}
	return m;
}

int main(){
	while( input() > 0 ){ std::cout << func() << std::endl; }
	return 0;
}