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>
#define INF 1e+18
#define int long long
using namespace std;

signed main(){
	int n,m,k,a[100010],dp[2][100010] = {},*now = dp[0],*nxt = dp[1],ma = 0;
	cin >> n >> m >> k;
	for(int i = 0;i < n;i++) cin >> a[i];
	for(int i = 1;i <= k;i++){
		deque<int> deq;
		for(int j = 0;j <= n;j++) nxt[j] = -INF;
		for(int j = 0;j < n;j++){
			while(!deq.empty() && now[deq.back()] <= now[j]) deq.pop_back();
			deq.push_back(j);
			nxt[j + 1] = now[deq.front()] + a[j] * i;
			if(deq.front() == j - m + 1) deq.pop_front();
		}
		swap(now,nxt);
	}
	for(int i = 0;i <= n;i++) ma = max(ma,now[i]);
	cout << ma << endl;
	return 0;
}