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 <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <deque>

using namespace std;

typedef long long ll;

int n, m, k;
ll a[111111];
ll dp4[333][111111];
int deq[333][111111];
int s[333], t[333];

int main(void) {
  scanf("%d%d%d", &n, &m, &k);
  for (int i = 0; i < n; i++) {
    scanf("%lld", a+i);
  }
  memset(dp4, -1, sizeof(dp4));
  for (int i = 0; i <= n; i++) {
    dp4[0][i] = 0;
    deq[0][t[0]++] = 0;
  }
  ll res = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = k-1; j >= 0; j--) {
      if (s[j] < t[j]) {
        dp4[j+1][i] = dp4[j][deq[j][s[j]]] + a[i-1]*(j+1);
        res = max(res, dp4[j+1][i]);
        while (s[j+1] < t[j+1] &&
               dp4[j+1][deq[j+1][t[j+1]-1]] <= dp4[j+1][i]) --t[j+1];
        deq[j+1][t[j+1]++] = i;
        if (i-m >= 0) {
          if (j > 0 && deq[j][s[j]] == i-m) {
            ++s[j];
          }
        }
      }
    }
  }
  printf("%lld\n", res);
  return 0;
}