Struck Out

There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.

Takahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i \times A_{p_i}.

He was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1,p_2,...,p_K. The only fact he remembers is that for every i (1 ≦ i ≦ K-1), 1 ≦ p_{i+1}-p_i ≦ M holds. Based on this fact, find the maximum possible total score for his throws.

Constraints

• 1 ≦ M ≦ N ≦ 100,000
• 1 ≦ K ≦ min(300,N)
• 1 ≦ A_i ≦ 10^{9}

Input

The input is given from Standard Input in the following format:

N M K A_1 A_2 … A_N

Output

Print the maximum possible total score for Takahashi's throws.

Examples

Input

5 2 3 10 2 8 10 2

Output

56

Input

5 5 2 5 2 10 5 9

Output

28

Input

10 3 5 3 7 2 6 9 4 8 5 1 1000000000

Output

5000000078

inputFormat

Input

The input is given from Standard Input in the following format:

N M K A_1 A_2 … A_N

outputFormat

Output

Print the maximum possible total score for Takahashi's throws.

Examples

Input

5 2 3 10 2 8 10 2

Output

56

Input

5 5 2 5 2 10 5 9

Output

28

Input

10 3 5 3 7 2 6 9 4 8 5 1 1000000000

Output

5000000078

样例

5 2 3
10 2 8 10 2

56