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;
typedef pair<long long int,int> pli;
const int MAXN = 100005;
const long long int INF = 1000000000000000000ll;
int A[MAXN];
long long int dp[2][MAXN];
int main()
{
	int n,m,k;
	scanf("%d %d %d", &n, &m, &k);
	for (int i = 1; i <= n; ++i)
		scanf("%d", &A[i]);
	memset(dp[0], 0, sizeof dp);
	for (int i = 1; i <= k; ++i)
	{
		int curr = i%2;
		int prev = 1 - curr;
		deque <pli> dq;
		for (int j = 0; j <= n; ++j)
		{
			if(j < i)
				dp[curr][j] = -INF;
			else
				dp[curr][j] = dq[0].first + 1ll*i*A[j];
			while(!dq.empty() && dq.back() < pli(dp[prev][j],j))
				dq.pop_back();
			dq.push_back(pli(dp[prev][j],j));
			while(!dq.empty() && dq[0].second <= j-m)
				dq.pop_front();
		}
	}
	long long int ans = -INF;
	for (int i = 0; i <= n; ++i)
		ans = max(ans, dp[k%2][i]);
	printf("%lld\n", ans);
	return 0;
}