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 CPP):

Solution:
#include <bits/stdc++.h>
int N, M, K, ptr[100009]; long long dp[309][100009];
int main() {
	scanf("%d %d %d", &N, &M, &K);
	for (int i = 0; i < N; i++) scanf("%lld", &dp[0][i]);
	for (int i = 1; i < K; i++) {
		int pl = 0, pr = 0;
		for (int j = 0; j < N; j++) {
			if (j >= i) dp[i][j] = dp[i - 1][ptr[pl]] + 1LL * (i + 1) * dp[0][j];
			if (ptr[pl] == j - M) pl++;
			while (pl < pr && dp[i - 1][ptr[pr - 1]] < dp[i - 1][j]) pr--;
			ptr[pr++] = j;
		}
	}
	printf("%lld\n", *std::max_element(dp[K - 1], dp[K - 1] + N));
	return 0;
}