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<iostream>
#include<deque>
using namespace std;
int N,M,K;
long A[1<<17];
deque<pair<long,int> >P[301];
int main()
{
	cin>>N>>M>>K;
	for(int i=0;i<N;i++)cin>>A[i];
	for(int i=0;i<K;i++)P[i].push_back(make_pair(-9e18,0));
	P[K].push_back(make_pair(0,0));
	for(int i=N;i--;)for(int j=1;j<=K;j++)
	{
		while(P[j].front().second-M>i)P[j].pop_front();
		pair<long,int>nxt;
		nxt.first=P[j].front().first+A[i]*j;
		nxt.second=i;
		while(!P[j-1].empty()&&P[j-1].back().first<=nxt.first)P[j-1].pop_back();
		P[j-1].push_back(nxt);
	}
	cout<<P[0][0].first<<endl;
}