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>

using namespace std;
int n;
int m;
int k;

#define MAX 100002



vector<long long int> V;

deque<pair<long long int,int> > mp[MAX];
int a[MAX];


int main(){
	cin >> n >> m >> k;
	for (int i = 0; i < n; i++){
		scanf("%d", &a[i]);
	}
	V.assign(k+1, -1);
	long long int ans = 0;
	for (int i = 0; i < n; i++){
		int mm = min(k, i + 1);
		for (int j = mm; j >=1; j--){
			while (!mp[j-1].empty() && mp[j-1].front().second < i - m){
				mp[j-1].pop_front();
			}
			long long int gt = 0;
			if(j>1)gt = mp[j-1].front().first;
			gt += (long long int)(a[i])*(long long int)(j);
			while (!mp[j].empty() && mp[j].back().first < gt){
				mp[j].pop_back();
			}
			mp[j].push_back(make_pair(gt,i));
			if (ans < gt){
				ans = gt;
			}
		}
	}
	printf("%lld\n", ans);
	return 0;
}