HardPrefix Sums2000 ms256 MB

Scholarship Window

Given daily practice minutes and a window size `k`, find the maximum total practice minutes over any consecutive `k` days.

Statement

Given daily practice minutes and a window size `k`, find the maximum total practice minutes over any consecutive `k` days.

Input

First line: `n k`. Second line: `n` integers.

Output

Print the maximum window sum.

Constraints

  • `1 <= k <= n <= 100000`

Examples

Example 1

Input

6 3
20 30 25 10 40 15

Output

75

The first three days total 75, which is the maximum.

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