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;

typedef long long ll;

ll solve(int n, int k) {
    ll a[n+1];
    a[0] = 0;
    for(int i=1;i<=n;++i){
        cin >> a[i];
        a[i] += a[i-1];
    }

    ll ans = 0LL;
    for(int i=1;i<=n-k;++i) {
        ans = max(ans, a[i+k-1]-a[i-1]);
    }
    return ans;
}

int main() {
    int n, k;

    while(cin >> n >> k && n) {
        cout << solve(n, k) << endl;
    }
}
