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<algorithm>
#include<string>
#include<map>
#include<set>
#include<stack>
#include<queue>
#include<math.h>
using namespace std;
typedef long long ll;
#define int long long
#define double long double
typedef vector<int> VI;
typedef pair<int, int> pii;
typedef vector<pii> VP;
typedef vector<string> VS;
typedef priority_queue<int> PQ;
template<class T>bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b < a) { a = b; return 1; } return 0; }
#define fore(i,a) for(auto &i:a)
#define REP(i,n) for(int i=0;i<n;i++)
#define eREP(i,n) for(int i=0;i<=n;i++)
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define eFOR(i,a,b) for(int i=(a);i<=(b);++i)
#define SORT(c) sort((c).begin(),(c).end())
#define rSORT(c) sort((c).rbegin(),(c).rend())
#define LB(x,a) lower_bound((x).begin(),(x).end(),(a))
#define UB(x,a) upper_bound((x).begin(),(x).end(),(a))
#define INF 1000000000
#define LLINF 9223372036854775807
#define mod 1000000007
#define eps 1e-12 
//priority_queue<int,vector<int>, greater<int> > q2;



signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	int N, M, K; cin >> N >> M >> K;
	M--;
	VI A(N);
	REP(i, N)cin >> A[i];
	vector<VI>dp(K + 1, VI(N + 1, 0));
	VI ma(N);

	eREP(i, N)eREP(j, K)dp[j][i] = 0;
	REP(i, N)dp[1][i] = A[i];

	deque<int>deq;
	REP(j, N) {
		while (!deq.empty() && dp[1][deq.back()] <= dp[1][j])deq.pop_back();
		deq.push_back(j);
		ma[j] = dp[1][deq.front()];
		if (deq.front() == j - M)deq.pop_front();
		//cout << ma[j] << endl;
	}

	eFOR(i, 2, K) {
		FOR(j, 1, N) {
			int tmp = ma[j - 1];
			dp[i][j] += tmp;
			if (dp[i][j] > 0)dp[i][j] += i * A[j];
		}

		deq.clear();
		REP(j, N) {
			while (!deq.empty() && dp[i][deq.back()] <= dp[i][j])deq.pop_back();
			deq.push_back(j);
			ma[j] = dp[i][deq.front()];
			if (deq.front() == j - M)deq.pop_front();
		}
	}

	int ans = -LLINF;
	eREP(i, N)chmax(ans, dp[K][i]);
	cout << ans << endl;
	return 0;
}