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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstdio>
#include <cstring>
#include <string>
#include <cmath>
#include <cassert>
#include <iostream>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
#include <set>
#include <map>
#include <bitset>
#include <functional>
using namespace std;

#define repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,n) repl(i,0,n)
#define mp(a,b) make_pair((a),(b))
#define pb(a) push_back((a))
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<((x))<<endl
#define fi first
#define se second

#define INF 2147483600

long dp[2][301];

int main(){
  int n,m,k;
  cin>>n>>m>>k;
  vector<long> vec(n);
  rep(i,n) scanf("%ld", &(vec[i]));

  long * prev = dp[0];
  long * crnt = dp[1];

  rep(i,n){
    fill(crnt, crnt+301, 0);
    crnt[1] = max(prev[1], vec[i]);
    repl(j,1,min(i+1,k+1)){
      // vec[i]までみてk個つかう
      crnt[j] = max(prev[j], prev[j-1]+j*vec[i]);
    }
//    rep(i,k+1) cout<<crnt[i]<<" "; cout<<endl;
    swap(crnt, prev);
  }

  cout << *max_element(prev, prev+k+1) << endl;

  return 0;
}