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;

const long long INF=1000000000000000000ll;

void slidemin(int n,int m,long long *A,long long *B)
{
  deque<int> Q;
  for(int i=0;i<n;i++){
    B[i]=(Q.empty()?INF:A[Q.front()]);
    while(!Q.empty()&&A[Q.back()]>=A[i]){
      Q.pop_back();
    }
    Q.push_back(i);
    if(i>=m&&Q.front()==i-m){
      Q.pop_front();
    }
  }
}

int main()
{
  int n,m,k;
  scanf("%d%d%d",&n,&m,&k);
  static long long a[100000];
  for(int i=0;i<n;i++){
    scanf("%d",a+i);
  }
  static long long X[2][100000];
  bool b=0;
  for(int j=0;j<n;j++){
    X[b][j]=-a[j];
  }
  for(int i=2;i<=k;i++){
    slidemin(n,m,X[b],X[!b]);
    for(int j=0;j<n;j++){
      X[!b][j]-=i*a[j];
      //printf("%d %d %lld\n",i,j,X[!b][j]);
    }
    b=!b;
  }
  long long ans=-INF;
  for(int i=0;i<n;i++){
    ans=max(ans,-X[b][i]);
  }
  printf("%lld\n",ans);
  return 0;
}