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 <bits/stdc++.h>

using namespace std;

int N, M, K;
int A[100001];
long long dp[301][100001];

struct smax
{
    long long q[100001];
    int w[100001];
    int h, t;
    void clear()
    {
        h=t=0;
    }
    void append(long long a, int b)
    {
        while(h<t && q[t-1]<=a)
            t--;
        w[t]=b;
        q[t++]=a;
    }
    void filter(int x)
    {
        while(h<t && w[h]<x)
            h++;
    }
    long long getmax()
    {
        return q[h];
    }
} dq;

int main()
{
    scanf("%d%d%d", &N, &M, &K);
    for(int i=1; i<=N; i++)
        scanf("%d", A+i), dp[1][i]=A[i];
    for(int i=2; i<=K; i++)
    {
        dq.clear();
        dq.append(dp[i-1][i-1], i-1);
        for(int j=i; j<=N; j++)
        {
            dq.filter(j-M);
            dp[i][j]=dq.getmax()+1LL*A[j]*i;
            dq.append(dp[i-1][j], j);
        }
    }
    printf("%lld\n", *max_element(dp[K]+1, dp[K]+1+N));
    return 0;
}