CODE FESTIVAL 2016 Tournament Round 3 (Parallel) - 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

Source: atcoder | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
from collections import deque
(N, M, K) = map(int, input().split())
A = list(map(int, input().split()))
dp = [0] * (N + 1)
for j in range(K):
	newDP = [0] * (N + 1)
	que = deque()
	for i in range(j, N - K + j + 1):
		while que and que[-1][0] < dp[i]:
			que.pop()
		que.append((dp[i], i))
		while que and que[0][1] <= i - M:
			que.popleft()
		newDP[i + 1] = que[0][0] + (j + 1) * A[i]
	dp = newDP
print(max(dp))


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()


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):
		while l < r and deq[l] < i - M:
			l += 1
		curr[i] = j * A[i] + prev[deq[l]] if i >= j - 1 and l < r else 0
		while l < r and prev[deq[r - 1]] <= prev[i]:
			r -= 1
		deq[r] = i
		r += 1
print(max(dp[K & 1]))