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 <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
#include <deque>
#include <map>
#include <set>
#include <cassert>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define sz(x) ((int)(x).size())
#define It iterator
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;

ll k,n,m, a[100001], dd[100001], d[100001]={0};

int main() {
    //freopen("test.in","r",stdin);
    cin>>n>>m>>k;
    rep(i,1,n+1) {cin>>a[i]; d[i]=a[i];}

    rep(K,2,k+1) {
        rep(i,1,n+1) dd[i]=d[i];
        rep(i,K,n+1) rep(j,1,m+1) if(i>j) dd[i]=max(dd[i], d[i-j]+a[i]*K);
        rep(i,1,n+1) d[i]=dd[i];
        rep(i,1,n+1) cout<<d[i]<<" ";
        cout<<endl;
    }

    ll ans=0;
    rep(i,1,n+1) ans=max(ans, d[i]);
    cout<<ans;
    return 0;
}