Problem:
Score : 700 points

Problem Statement

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}

Partial Scores

In the test set worth 100 points, M = N.

In the test set worth another 200 points, N ≦ 300 and K ≦ 30.

In the test set worth another 300 points, K ≦ 30.

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.

Sample Input 1

5 2 3
10 2 8 10 2

Sample Output 1

56

The total score is maximized when panels 1,3 and 4 are hit, in this order.

Sample Input 2

5 5 2
5 2 10 5 9

Sample Output 2

28

This case satisfies the additional constraint M = N for a partial score.

Sample Input 3

10 3 5
3 7 2 6 9 4 8 5 1 1000000000

Sample Output 3

5000000078

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
long long MAX(long long a,long long b){return a<b?b:a;}
long long d[310][100010]={};
int main(){
  long long n,m,k,a[100010],i,j,max,l;
  scanf("%lld %lld %lld",&n,&m,&k);
  for(i=0;i<n;i++)scanf("%lld",&a[i]);
  for(i=0;i<k;i++){
    for(j=0;j<n;j++){
      for(l=max=0;l<m;l++)max=MAX(max,d[i][j-m+1]);
      d[i+1][j+1]=MAX(d[i+1][j+1],max+(i+1)*a[j]);
    }
  }
 /* for(i=0;i<=k;i++){
    for(j=0;j<=n;j++)printf("%lld ",d[i][j]);printf("\n");
}//*/
  printf("%lld\n",d[k][n]);
  return 0;
}