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 <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long ll;

ll N,K;
ll a[100005];

int main(){
  while(scanf("%lld%lld", &N,&K) && N||K){
    for(int i=0;i<N;i++) scanf("%lld", &a[i]);
    ll sum = 0, res;
    for(ll i=0;i<K;i++) sum += a[i];
    res = sum;
    for(ll i=K;i<N;i++){
      sum -= a[i-K];
      sum += a[i];
      res = max(res, sum);
    }
    printf("%lld\n", res);
  }
  return 0;
}