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>
using namespace std;
typedef long long ll;

int N,M,K;
ll A[100010],dp[100010][310] = {{0}},D[100010] = {0};

int main(){
	cin >> N >> M >> K;
	for(int i=1;i<=N;i++){
		cin >> A[i];
		dp[i][1] = A[i];
	}
	int s = 0,t = 0;
	for(ll j=2;j<=K;j++){
		for(int i=1;i<N;i++){
			while(s<t && dp[D[t-1]][j-1]<=dp[i][j-1]) t--;
			D[t] = i;
			t++;
			if(j-1<=i){
				int m = D[s];
				dp[i+1][j] = dp[m][j-1] + j*A[i+1];
				if(i>=M && D[s]==i-M+1) s++;
			}
		}
		for(int i=0;i<=N;i++) D[i] = 0;
		s = 0; t = 0;
	}
	ll ans = 0;
/*	for(int j=1;j<=K;j++){
		for(int i=1;i<=N;i++){
			cout << dp[i][j] << (i!=N? " ":"\n");
		}
	}
*/	for(int i=K;i<=N;i++) ans = max(ans,dp[i][K]);
	cout << ans << endl;
}