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 <algorithm>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <vector>

using namespace std;
using ll = long long;

#define all(c) (c).begin(), (c).end()
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define pb(e) push_back(e)
#define mp(a, b) make_pair(a, b)
#define fr first
#define sc second

const ll INF = 1e9;
const ll MOD = 1e9 + 7;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

ll dp[100005][301];
int N, M, K;
int A[100005];
ll dfs(int i, int k) {
    if (i == N) {
        if (k == 0)
            return 0;
        else
            return -INF;
    }
    if (dp[i][k] != -1) return dp[i][k];
    ll ret = dfs(i + 1, k);
    if (k) ret = max(ret, dfs(i + 1, k - 1) + (K - k + 1) * A[i]);
    return dp[i][k] = ret;
}
int main() {
    memset(dp, -1, sizeof(dp));
    cin >> N >> M >> K;
    rep(i, N) cin >> A[i];
    if (N != M) return 0;
    cout << dfs(0, K) << endl;
    return 0;
}