chunlian

Problem Description

Guangxuan has been shopping for Chunlians during CNY. When he entered the shop, he found N Chunlians hung on the wall, from left to right. Each Chunlian had a certain value P_i.

He needs to buy C Chunlians for his family. Furthermore, due to his laziness, he wants to select the Chunlians such that no two Chunlians (including non-consecutive ones) are more than distance K apart from one another on the wall.

Help Guangxuan determine the maximum value he can obtain.

Input

The first line of input will contain three integers, N, C and K.

The second line of input will contain N integers, representing the array P.

Output

The output should contain one integer, representing the maximum value Gug can obtain.

Limits

For all subtasks: 1 ≤ C ≤ N, C - 1 ≤ K < N, 1 ≤ P_i ≤ 10⁹.

Subtask 1 (13%): 1 ≤ N ≤ 20.

Subtask 2 (15%): 1 ≤ N ≤ 200.

Subtask 3 (17%): 1 ≤ N ≤ 1000.

Subtask 4 (12%): 1 ≤ N ≤ 300000, 1 ≤ P_i ≤ 2.

Subtask 5 (14%): 1 ≤ N ≤ 300000, 1 ≤ C ≤ 2.

Subtask 6 (29%): 1 ≤ N ≤ 300000.

Subtask 7 (0%): Sample Testcases

Sample Testcase 1

Input

5 2 3
8 1 2 3 5

Output

11

Sample Testcase 2

Input

7 3 4
5 7 1 6 3 5 9

Output

20