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;

typedef long long LL;

struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;
#define fin "\n"


#define FOR(i,bg,ed) for(int i=(bg);i<(ed);i++)
#define REP(i,n) FOR(i,0,n)

template <typename T>
inline void chmin(T &l,T r){l=min(l,r);}

template <typename T>
inline void chmax(T &l,T r){l=max(l,r);}

LL deq[300000];
void ch(vector<LL>& a,vector<LL>& b,vector<LL>& A,LL M,LL m){
    int N=A.size();
    int s=0,t=0;
    REP(i,N){
        while(s<t&&i-deq[s]>M)s++;
        if(s==t)b[i]=-1e16;
        else{
            b[i]=a[deq[s]]+A[i]*m;
        }
        while(s<t&&a[deq[t-1]]<=a[i])t--;
        deq[t++]=i;
    }
}

int main(){
    LL N,M,K;
    cin>>N>>M>>K;
    vector<LL> A(N);
    for(auto &it:A)cin>>it;
    vector<LL> dp=A;
    FOR(i,1,K){
        //for(auto &it:dp)cout<<it<<" ";cout<<endl;
        vector<LL> nxt(N);
        ch(dp,nxt,A,M,i+1);
        swap(dp,nxt);
    }
    LL res=0;
    for(auto &it:dp)chmax(res,it);
    cout<<res<<endl;
    return 0;
}