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;

#define INF_LL (int64)1e18
#define INF (int32)1e9
#define REP(i, n) for(int i = 0;i < (n);i++)
#define FOR(i, a, b) for(int i = (a);i < (b);i++)
#define all(x) x.begin(),x.end()
#define fs first
#define sc second

using int32 = int_fast32_t;
using uint32 = uint_fast32_t;
using int64 = int_fast64_t;
using uint64 = uint_fast64_t;
using PII = pair<int32, int32>;
using PLL = pair<int64, int64>;

const double eps = 1e-6;

template<typename A, typename B>inline void chmin(A &a, B b){if(a > b) a = b;}
template<typename A, typename B>inline void chmax(A &a, B b){if(a < b) a = b;}

const int64 mod = 1e9+7;

/*
int main(void){
	int32 N;
	cin >> N;
	vector<int64> v(N);
	REP(i, N) cin >> v[i];

	int64 maxi = 0;
	int64 res = 0;
	REP(i, N){
		int64 cnt = (v[i]-1)/(maxi+1);
		if(cnt){ res += cnt; chmax(maxi, 1); }
		else maxi = v[i];
	}
	cout << res << endl;
}
*/

int64 A[112345];
deque<PLL> deq[301];

int main(void){
	int32 M, N, K;
	cin >> N >> M >> K;
	REP(i, N) cin >> A[i];

	REP(i, N){
		for(int32 j = K-1;j >= 1;j--){
			while(deq[j-1].size() && i-deq[j-1].front().sc > M) deq[j-1].pop_front();
			if(deq[j-1].empty()) continue;
			int64 val = deq[j-1].front().fs+A[i]*(j+1);
			while(deq[j].size() && val > deq[j].back().fs) deq[j].pop_back();

			deq[j].push_back(PLL(val, i));
		}
		while(deq[0].size() && A[i] > deq[0].back().fs) deq[0].pop_back();
		deq[0].push_back(PLL(A[i], i));
	}

	cout << deq[K-1].front().fs << endl;
}