Problem: 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}

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.

Examples

Input

5 2 3
10 2 8 10 2


Output

56


Input

5 5 2
5 2 10 5 9


Output

28


Input

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


Output

5000000078

Solution (in CPP):

Solution:
#include <iostream>

using namespace std;

typedef long long ll;

ll dp_prev[100000];
ll dp_cur[100000];
ll deq[100000];

ll N, M, K;

void copy_dp(){
    for(int i = 0; i < N; i++){
        dp_prev[i] = dp_cur[i];
    }
}

int main(){
    cin >> N >> M >> K;
    ll A[100000];
    for(int i = 0; i < N; i++) {
        cin >> A[i];
        dp_cur[i] = A[i];
    }
    for(ll i = 1; i < K; i++){
        copy_dp();
        for(int j = 0; j < i; j++) dp_cur[j] = 0;
        int s = 0, t = 0;
        for(int j = 0; j < N-1; j++){
            while(s < t && dp_prev[deq[t-1]] <= dp_prev[j]) t--;
            deq[t++] = j;
            if(j+1 >= i) dp_cur[j+1] = (i+1)*A[j+1]+dp_prev[deq[s]];
            if(j-M+1 >= 0 && deq[s] == (j-M+1)) s++;
        }
    }
    ll ans = 0;
    for(int i = 0; i < N; i++) ans = max(ans, dp_cur[i]);
    cout << ans << endl;
}