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;

const ll MAXN = 111000;
const ll MAXK = 333;
ll dp[MAXK][MAXN];
ll arr[MAXN];

void solve(ll test_num) {
  (void) test_num;
  ll N, M, K;
  cin >> N >> M >> K;
  for (ll i = 1; i <= N; ++i) {
    cin >> arr[i];
  }
  memset(dp, 0xC0, sizeof(dp));
  for (ll j = 1; j <= N; ++j)
    dp[1][j] = arr[j];
  deque<ll> deq;
  for (ll i = 2; i <= K; ++i) {
    deq.clear();
    for (ll j = i, fr = 1; j <= N; ++j) {
      for (; fr < j; ++fr) {
        while (!deq.empty() && dp[i - 1][fr] >= dp[i - 1][deq.back()])
          deq.pop_back();
        deq.push_back(fr);
      }
      while (deq.front() < j - M)
        deq.pop_front();
      dp[i][j] = i * arr[j] + dp[i - 1][deq.front()];
    }
  }
  const ll res = *max_element(dp[K], dp[K] + N + 1);
  cout << res << endl;
}

void init() {

}

int main() {
#ifdef AZN
  const auto start_time = chrono::system_clock::now();
  freopen("/home/azneye/Documents/Stuff/input.txt", "r", stdin);
#endif
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  init();
  ll tests = 1;
  //cin >> tests;
  for (ll test = 1; test <= tests; ++test) {
    solve(test);
  }
#ifdef AZN
  cerr << "Took: " << ((chrono::system_clock::now() - start_time).count() / 1e9) << " s" << endl;
#endif
  return 0;
}