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 <algorithm>
#include <iostream>
#include <queue>
using namespace std;

const int N = (int) 1e5;
long long f[N], g[N + 1];
int a[N];

int main() {
    ios::sync_with_stdio(false);
    int n, m, k; cin >> n >> m >> k;
    for (int i = 0; i < n; ++i) cin >> a[i];
    for (int t = k; t >= 1; --t) {
        for (int i = 0; i < n; ++i) g[i] = f[i];
        deque<int> q;
        q.push_back(n);
        if (t != k) g[n] = -1e18;
        for (int i = n - 1; i >= 0; --i) {
            while (!q.empty() && q.front() - i > m) q.pop_front();
            f[i] = g[q.front()] + 1LL * t * a[i];
            while (!q.empty() && g[i] >= g[q.back()]) q.pop_back();
            q.push_back(i);
        }
    }
    cout << *max_element(f, f + n) << endl;
    return 0;
}