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>
#define all(v) v.begin(),v.end()
using namespace std;
typedef long long ll;
const ll INF=1000000010;
const ll MOD=1000000007;
const ll LINF=4000000000000000000;
const long double EPS=1e-9;
typedef pair<int,int> P;
ll dp[100010];
int main(){
    int N,M,K;cin>>N>>M>>K;
    ll a[100010];
    for(int i=1;i<=N;i++)cin>>a[i],dp[i]=a[i];
    for(int i=2;i<=K;i++){
        deque<int> deq;
        ll dp2[100010]={};
        for(int j=i;j<=N;j++){
            while(!deq.empty()&&dp[deq.back()]<=dp[j-1])deq.pop_back();
            deq.push_back(j-1);
            dp2[j]=dp[deq.front()];
            while(!deq.empty()&&deq.front()<=j-M)deq.pop_front();
        }
        for(int j=1;j<=N;j++)dp[j]=dp2[j]+a[j]*i;
    }
    ll ans=0;
    for(int i=1;i<=N;i++){
        ans=max(dp[i],ans);
    }
    cout<<ans<<endl;
}