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)

// 基本テンプレート
 
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
using namespace std;
 
#define rep(i,a,n) for(int (i)=(a); (i)<(n); (i)++)
#define repq(i,a,n) for(int (i)=(a); (i)<=(n); (i)++)
#define repr(i,a,n) for(int (i)=(a); (i)>=(n); (i)--)
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define int long long int
 
template<typename T> void chmax(T &a, T b) {a = max(a, b);}
template<typename T> void chmin(T &a, T b) {a = min(a, b);}
template<typename T> void chadd(T &a, T b) {a = a + b;}
 
typedef pair<int, int> pii;
typedef long long ll;
 
int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
const ll INF = 1001001001001001LL;
const ll MOD = 1000000007LL;

int dp[2][100010];
 
signed main() {
    int N, M, K; cin >> N >> M >> K;
    vector<int> A(N);
    for(int i=0; i<N; i++) cin >> A[i];

    memset(dp, 0, sizeof(dp));
    int ans = 0;
    for(int k=0; k<K; k++) {
        int cur = k%2, nxt = 1 - cur;

        deque< pair<int, int> > deq;
        for(int i=0; i<N; i++) {
            // dp[k-1][i-1] から dp[k-1][i-M] までを見る
            int num = k + 1;
            int prev_max = (deq.empty() ? 0 : deq.front().first);
            dp[nxt][i] = prev_max + A[i] * num;
            // printf("dp[k = %lld][i = %lld] = %lld\n", k+1, i+1, dp[nxt][i]);
            if(k + 1 == K) chmax(ans, dp[nxt][i]);

            int lb = i+1-M, val = dp[cur][i];
            while(deq.size() && (deq.front().second < lb || deq.front().first < val)) deq.pop_front();
            while(deq.size() && deq.back().first < val) deq.pop_back();

            pair<int, int> elem = make_pair(val, i);
            if(deq.empty() || deq.front().first < val) deq.push_front(elem);
            else deq.push_back(elem);

            dp[cur][i] = 0;
        }
    }
    cout << ans << endl;
    return 0;
}