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>
#define sp ' '
#define mkp make_pair
#define intmax 2147483647
#define llmax 9223372036854775807
#define lP pair<ll,ll>
#define iP pair<int,int>
typedef long long ll;
using namespace std;
const int mod = 1000000007, mod998 = 998244353;

int N, M, K;
ll DP[100000][301], A[100000], res;

int main() {
	cin >> N >> M >> K;
	for (int i = 0; i < N; ++i) {
		cin >> A[i];
	}
	for (int i = 1; i <= K; ++i) {
		deque<pair<int, ll>>q;
		q.push_back(mkp(i - 2, i == 1 ? 0 : DP[i - 2][i - 1]));
		for (int j = i - 1; j < N; ++j) {
			while (q.back().first + M < j)q.pop_back();
			DP[j][i] = q.back().second + A[j] * i;
			while (!q.empty() && q.front().second < DP[j][i - 1])q.pop_front();
			q.push_front(mkp(j, DP[j][i - 1]));
		}
	}
	for (int i = 0; i < N; ++i) {
		res = max(res, DP[i][K]);
	}
	cout << res << endl;
}