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;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

ll to[101010],from[101010];
int A[101010], deq[101010];

int main(){
  int N,M,K; cin>>N>>M>>K;
  for(int i=1;i<=N;i++){
    cin>>A[i];
    from[i]=1LL*A[i];
  }
  for(int i=2;i<=K;i++){
    int s=0,t=0;
    deq[s]=0;
    for(int j=1;j<i;j++){
      while(s<t&&from[deq[t-1]]<=from[j]) t--;
      deq[t++]=j;
    }
    for(int j=i;j<=N;j++){
      to[j]=1LL*A[j]*i+from[deq[s]];
      if(j-M>=1&&deq[s]==j-M) s++;
      while(s<t&&from[deq[t-1]]<=from[j]) t--;
      deq[t++]=j;
    }
    swap(to,from);
  }
  ll ans=0;
  rep(i,N) ans=max(ans,from[i+1]);
  cout<<ans<<endl;
  return 0;
}