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;

template< typename T >
vector< T > slide_min(const vector< T > &v, int k)
{
  deque< int > deq;
  vector< T > ret;
  for(int i = 0; i < v.size(); i++) {
    while(!deq.empty() && v[deq.back()] <= v[i]) {
      deq.pop_back();
    }
    deq.push_back(i);
    if(i - k + 1 >= 0) {
      ret.emplace_back(v[deq.front()]);
      if(deq.front() == i - k + 1) deq.pop_front();
    }
  }
  return (ret);
}

using int64 = long long;

int main()
{
  int N, M, K, A[100000];

  cin >> N >> M >> K;
  for(int i = 0; i < N; i++) {
    cin >> A[i];
  }

  vector< int64 > dp(N);
  for(int i = 0; i < N; i++) {
    dp[i] = A[i];
  }
  for(int i = 1; i < K; i++) {
    vector< int64 > dp2(N);
    reverse(begin(dp), end(dp));
    dp.resize(N + M - 1);
    reverse(begin(dp), end(dp));
    auto p = slide_min(dp, M);


    for(int j = i; j < N; j++) {

      dp2[j] = max(dp2[j], p[j - 1] + 1LL * (i + 1) * A[j]);

    }
    dp.swap(dp2);
  }

  cout << *max_element(begin(dp), end(dp)) << endl;

}