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;
const int maxn = 100100, maxk = 303;
long long dp[maxk][maxn], a[maxn];
long long dq[maxn];
int pl, pr;
void clear(){
	pl = 0;
	pr = -1;
}
void add(long long v){
	while(pl <= pr && dq[pr] < v) pr--;
	dq[++pr] = v;
}
void del(long long v){
	if(dq[pl] == v) pl++;
}
long long best(){
	assert(pl <= pr);
	return dq[pl];
}
int main(){
	int n, m, k; cin >> n >> m >> k;
	for(int i = 0; i < n; i++) cin >> a[i];
	for(int i = 0; i < n; i++) dp[1][i] = a[i];
	for(int i = 2; i <= k; i++){
		clear();
		add(dp[i - 1][i - 2]);
		for(int j = i - 1; j < n; j++){
			if(j - m - 1 >= i - 2) del(dp[i - 1][j - m - 1]);
			dp[i][j] = best() + i * a[j];
			add(dp[i - 1][j]);
		}
	}
	long long ans = 0;
	for(int i = 0; i < n; i++) ans = max(ans, dp[k][i]);
	cout << ans << endl;
	return 0;
}