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 rep(i,n)for(int i=0;i<(n);i++)
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define MOD 1000000007
#define EPS (1e-10)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

ll dp[301][100000];
ll a[100000];

signed main(){
	int n,m,k;scanf("%d%d%d",&n,&m,&k);
	rep(i,n){
		scanf("%lld",&a[i]);
		dp[0][i]=a[i];
	}
	for(int i=1;i<k;i++){
		deque<ll>que;
		for(int j=1;j<n;j++){
			while(!que.empty()&&que.front()<j-m)que.pop_front();
			if(dp[i-1][j-1]){
				while(!que.empty()&&dp[i-1][que.back()]<=dp[i-1][j-1])que.pop_back();
				que.push_back(j-1);
			}
			if(!que.empty())dp[i][j]=dp[i-1][que.front()]+(i+1)*a[j];
		}
	}
	ll Max=0;
	rep(i,n)Max=max(Max,dp[k-1][i]);
	cout<<Max<<endl;
}