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>
#include<map>
using namespace std;
typedef long long int LL;
typedef pair<LL,int> P;
LL t[100005];
LL dp[100005];
deque<P> d1;
int main(){
	int m,n,p;
	LL i,j,k;
	LL a,b,c;
	LL s=0;
	cin>>n>>m>>p;
	for(i=0;i<n;i++){
		cin>>t[i];
		dp[i+1]=t[i];
	}
	for(i=2;i<=p;i++){
		for(j=0;j<n;j++){
			while(!d1.empty()){
				a=d1.front().first,b=d1.front().second;
				if(j<=b+m)break;
				else d1.pop_front();
			}
			if(d1.empty() || a==0)c=0;
			else c=a+t[j]*i;
			while(!d1.empty() && d1.back().first<dp[j+1])d1.pop_back();
			d1.push_back(make_pair(dp[j+1],j));
			dp[j+1]=c;
		}
		d1.clear();
		//for(j=0;j<=n;j++){
			//cout<<dp[j]<<" ";
		//}
		//cout<<endl;
	}
	for(i=0;i<=n;i++){
		if(s<dp[i])s=dp[i];
	}
	cout<<s<<endl;
	return 0;
}