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 Int = long long;
//INSERT ABOVE HERE
signed main(){
  Int n,m,k;
  cin>>n>>m>>k;
  vector<Int> a(n);
  for(Int i=0;i<n;i++) cin>>a[i];
  vector<Int> dp(a);
  for(Int i=1;i<k;i++){
    vector<Int> nx(n,0);
    deque<Int> d;
    for(Int j=i;j<n;j++){
      while(!d.empty()&&d.front()<j-m) d.pop_front();
      while(!d.empty()&&dp[d.back()]<=dp[j-1]) d.pop_back();
      d.emplace_back(j-1);
      nx[j]=dp[d.front()];
    }
    swap(dp,nx);
    for(Int j=0;j<n;j++) dp[j]+=(i+1)*a[j];
  }
  cout<<*max_element(dp.begin(),dp.end())<<endl;
  return 0;
}