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;

using ll=long long;
int main(){
    int n,m,k;
    cin>>n>>m>>k;
    vector<ll> a(n);
    for(int i=0;i<n;i++) cin>>a[i];
    vector<vector<ll>> dp(k+1,vector<ll>(n+1,0));
    for(int i=0;i<k;i++){
        deque<ll> deq;
        deque<int> ids;
        deq.push_back(dp[i][i]);
        ids.push_back(i);
        for(int j=i+1;j<=n;j++){
            while(m<j-ids.front()){
                deq.pop_front();
                ids.pop_front();
            }
            dp[i+1][j]=deq.front()+(i+1)*a[j-1];
            while(!deq.empty()){
                if(deq.back()<dp[i][j]) deq.pop_back(),ids.pop_back();
                else break;
            }
            deq.push_back(dp[i][j]);
            ids.push_back(j);
        }
    }    

    cout<<*max_element(dp[k].begin(),dp[k].end())<<endl;
    return 0;
}