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 <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <map>
#include <set>
#include <string>
#include <cstdlib>
#include <ctime>
#include <deque>
using namespace std;

int n, m, k;
int a[110000];
long long dp[110000][310];
int q[110000], h[110000], xx[110000][310];

int main() {
	scanf("%d%d%d", &n, &m, &k);
	for (int i = 1; i <= n; i++)
		scanf("%d", &a[i]);
	for (int i = 1; i <= k; i++)
		dp[0][i] = -1e18;
	for (int i = 0; i <= k; i++)
		q[i] = h[i] = 1, xx[i][1] = 0;
	for (int i = 1; i <= n; i++) {
		for (int j = 0; j <= k; j++) {
			while (q[j] <= h[j] && xx[j][q[j]] < i - m)
				q[j] += 1;
			dp[i][j + 1] = dp[xx[j][q[j]]][j] + 1LL * (j + 1) * a[i];
		}
		for (int j = 0; j <= k; j++) {
			while (q[j] <= h[j] && dp[xx[j][h[j]]][j] <= dp[i][j])
				h[j] -= 1;
			xx[j][++h[j]] = i;
				// q[j] += 1;
		}
	}
	long long ans = -1e18;
	for (int i = 1; i <= n; i++)
		ans = max(ans, dp[i][k]);
	cout << ans << endl;
}