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:
#define  _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <cstring>
#include <queue>
#include <stack>
#include <math.h>
#include <iterator>
#include <vector>
#include <string>
#include <set>
#include <math.h>
#include <iostream>
#include <random>
#include<map>
#include <iomanip>
#include <time.h>
#include <stdlib.h>
#include <list>
#include <typeinfo>
#include <list>
#include <set>
#include <cassert>
#include<fstream>
#include <unordered_map>
#include <cstdlib>
#include <complex>
#include <cctype>
#include <bitset>
using namespace std;
typedef string::const_iterator State;
#define Ma_PI 3.141592653589793
#define eps 0.00000001
#define LONG_INF 1e18
#define GOLD 1.61803398874989484820458
#define MAX_MOD 1000000007
#define MOD 998244353
#define seg_size 262144
#define REP(a,b) for(long long a = 0;a < b;++a)
vector<complex<double>>  DFT(vector<complex<double>> a) {
	int n = a.size();
	if (n == 1) return a;
	vector<complex<double>> a0(n / 2), a1(n / 2);
	REP(i, n) {
		if (i % 2 == 0) {
			a0[i / 2] = a[i];
		}
		else {
			a1[i / 2] = a[i];
		}
	}
	vector<complex<double>> inversed_a0 = DFT(a0), inversed_a1 = DFT(a1);
	vector<complex<double>> inversed_a(n);
	for (int i = 0; i < n; ++i) {
		complex<double> zeta = complex<double>(cos(2 * Ma_PI * i / n), sin(2 * Ma_PI * i / n));
		inversed_a[i] = inversed_a0[i % (n / 2)] + zeta * inversed_a1[i % (n / 2)];
	}
	return inversed_a;
}
vector<complex<double>> IDFT(vector<complex<double>> inversed_a) {
	int n = inversed_a.size();
	vector<complex<double>> now = DFT(inversed_a);
	reverse(now.begin(), now.end());
	for (int q = now.size() - 1; q >= 1; --q) {
		swap(now[q], now[q - 1]);
	}
	REP(i, n) {
		now[i] /= complex<double>(n, 0);
	}
	return now;
}
vector<complex<double>> conv(vector<complex<double>> a, vector<complex<double>> b) {
	int deg = a.size() + b.size() - 1;
	int n = 1;
	while (n < deg) n <<= 1;
	a.resize(n);
	b.resize(n);
	vector<complex<double>> inversed_a = DFT(a),inversed_b = DFT(b);
	vector<complex<double>> inversed_c(n);
	REP(i, n) {
		inversed_c[i] = inversed_a[i] * inversed_b[i];
	}
	return IDFT(inversed_c);
}

vector<long long> inputs;
long long dp[200000][301] = {};
deque<long long> tmp[301];

void inserting(long long value,long long itr) {
	while (tmp[itr].empty() == false && dp[tmp[itr].back()][itr] < dp[value][itr]) {
		tmp[itr].pop_back();
	}
	tmp[itr].push_back(value);
}

int main() {
	int n, m, k;
	cin >> n >> m >> k;
	REP(i, n) {
		long long a;
		cin >> a;
		inputs.push_back(a);
	}
	REP(i, 200000) {
		REP(q, 301) {
			dp[i][q] = -LONG_INF;
		}
	}
	REP(i, n) {
		for (long long q = k - 1; q >= 1; --q) {
			if (tmp[q].empty() == true) continue;
			while(tmp[q].front() == i - m - 1) {
				tmp[q].pop_front();
			}
			dp[i][q + 1] = dp[tmp[q].front()][q] + inputs[i] * (q + 1LL);
			inserting(i, q + 1);
		}
		dp[i][1] = inputs[i];
		inserting(i, 1);
	}
	long long ans = 0;
	REP(i, n) {
		ans = max(ans, dp[i][k]);
	}
	cout << ans << endl;
	return 0;
}