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>
#define MIN -1000000000000000000
using namespace std;

int input[100010];

int main() {
	while(1){
		int N,K;
		long long int sum=0,nummax=MIN;
		cin >> N >> K;
		if(N==0 && K==0)break;
		
		for(int i=0;i<100010;i++)input[i]=0;
		
		for(int i=0;i<N;i++){
			cin >> input[i];
			sum+=input[i];
			if(i+1>=K){
				sum-=input[i-K];
				if(nummax<sum)nummax=sum;
			}
		}
		cout << nummax <<endl;
	}
	return 0;
}