Maximum Information (DA)

You must choose a starting point and collect its security value, then repeatedly jump +k and collect the value where you land, stopping only when the next jump would go out of bounds. You cannot stop early or choose nothing, and values may be negative; find the total for the best starting point.

输入格式

The first line contains n k, followed by n security values; original bounds 1≤n≤1000000, 1≤k≤n, −1000≤security[i]≤1000.

输出格式

Output a single integer answer.

样例 1

输入：

5 2
2 -3 4 6 1

输出：

7

样例 2

输入：

2 1
5 -10

输出：

-5

样例 3

输入：

3 2
-5 -2 -3

输出：

-2

样例说明

The outputs of the three public examples are, in order: 7; -5; -2. These answers have been checked by independent enumeration or direct simulation.