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 <iostream>
#include <vector>
#include <deque>

using namespace std;



int main(){
	int N, M, K;
	while(cin >> N >> M >> K){
		vector<long long> A(N);
		for(auto& t : A) cin >> t;
		auto dp = A;
		for(int i=2;i<=K;i++){
			deque<pair<int, long long>> qu;
			for(int j=0;j<N;j++){
				long long cur = 0;
				if(!qu.empty()) cur = qu.front().second;
				if(!qu.empty() && qu.front().first + M == j) qu.pop_front();
				while(!qu.empty() && qu.back().second <= dp[j]) qu.pop_back();
				qu.emplace_back(j, dp[j]);
				if(cur > 0) cur += i * A[j];
				dp[j] = cur;
			}
		}
		long long res = 0;
		for(auto& t : dp) res = max(res, t);
		cout << res << endl;
	}
}