Problem: 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

Solution (in PYTHON3):

Solution:
from sys import stderr

def reads():
  return [int(x) for x in input().split()]

N, M, K = reads()
A = reads()

dp = [[0] * N, list(A)]
deq = [0] * N
for j in range(2, K+1):
  l = r = 0
  b = j & 1
  prev = dp[1-b]; curr = dp[b]
  for i in range(N):
    # pop
    while l < r and deq[l] < i-M:
      l += 1
    # max
    curr[i] = (j * A[i] + prev[deq[l]]) if (i >= j-1 and l < r) else 0
    # append
    while l < r and prev[deq[r-1]] <= prev[i]:
      r -= 1
    deq[r] = i; r += 1

print(max(dp[K & 1]))