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 lli;
typedef double lld;
typedef vector<lli> vll;
typedef vector<bool> vbl;
typedef vector<double> vdl;
typedef vector<vector<lli>> mat;
typedef vector<vdl> mad;
typedef unordered_map<lli,unordered_map<lli,lli>> graph;
typedef complex<double> cmp;
typedef vector<cmp> vcl;



mat dp;

lli n,m,k;
vll a;
deque<lli> dq;

int main(){
  cin >> n >> m >> k;
  a = vll(n+1);
  for(lli i = 1;i <= n;i++) cin >> a[i];
  dp = mat(k+1,vll(n+1));
  for(lli i = 1;i <= k;i++){
    dq = deque<lli>();
    dq.push_back(i-1);
    for(lli j = i;j <= n;j++){
      while(dq.front() < j-m) dq.pop_front();
      dp[i][j] = dp[i-1][dq.front()]+i*a[j];
      while(dq.size() > 0 && dp[i-1][dq.back()] < dp[i-1][j]) dq.pop_back();
      dq.push_back(j);
      // dp[i][j] = *max_element(dp[i-1].begin()+max(i-1,j-m),dp[i-1].begin()+j-1)+i*a[j];
    }
  }
  cout << *max_element(dp[k].begin(),dp[k].end()) << endl;

}