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:
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
    Q0 = [0]*N; Q1 = [0]*N
    for k in range(2, K+1):
        s = t = 0

        for i in range(k-1, N):
            a = S[i-1]
            while s < t and Q1[t-1] <= a:
                t -= 1
            Q0[t] = i-1; Q1[t] = a
            t += 1

            T[i] = Q1[s] + A[i]*k

            if s < t and Q0[s] <= i-M:
                s += 1
        S, T = T, S
    print(max(S))
solve()