Problem:
Score : 700 points

Problem Statement

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}

Partial Scores

In the test set worth 100 points, M = N.

In the test set worth another 200 points, N ≦ 300 and K ≦ 30.

In the test set worth another 300 points, K ≦ 30.

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.

Sample Input 1

5 2 3
10 2 8 10 2

Sample Output 1

56

The total score is maximized when panels 1,3 and 4 are hit, in this order.

Sample Input 2

5 5 2
5 2 10 5 9

Sample Output 2

28

This case satisfies the additional constraint M = N for a partial score.

Sample Input 3

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

Sample Output 3

5000000078

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

from collections import deque
import sys
def solve():
    readline = sys.stdin.readline

    N, M, K = map(int, readline().split())
    *A, = map(int, readline().split())

    S = A[:]
    T = [0]*N
    zeros = [0]*N
    for k in range(K-1):
        que0 = deque()
        que1 = deque()
        T[:k+1] = zeros[:k+1]

        for i in range(k, N-1):
            a = S[i]
            while que1 and que1[-1] <= a:
                que0.pop()
                que1.pop()
            que0.append(i)
            que1.append(a)

            T[i+1] = que1[0] + A[i+1]*(k+2)

            if que0 and que0[0] <= i+1-M:
                que0.popleft()
                que1.popleft()
        S, T = T, S
    print(max(S))
solve()