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 <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
//#include <utility>
//#include <memory>
//#include <functional>
//#include <deque>
//#include <cctype>
//#include <ctime>
//#include <numeric>
//#include <list>
//#include <iomanip>

//#if __cplusplus >= 201103L
//#include <array>
//#include <tuple>
//#include <initializer_list>
//#include <forward_list>
//
//#define cauto const auto&
//#else

//#endif

using namespace std;


typedef unsigned long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<ll> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()) {
	v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t) {
	stringstream ss;
	ss << f;
	ss >> t;
}

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x)
#define debug(x)
#endif

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)


template<typename T>
class RMQ {
public:
	std::vector<T> data;
	std::vector<std::vector<int> > block;
	std::vector<int> sblock;
	std::vector<int> lookup;
	int N;
	int lg;
	int min(int a, int b) {
		return data[b] >= data[a] ? b : a;
	}
	RMQ() {}
	RMQ(std::vector<T> &t) {
		data = t;
		N = data.size();
		
		// lg = sizeof(T) * 8 - __builtin_clz(N);
		lg = 32 - __builtin_clz(N);

		block.assign((N + lg - 1) / lg, std::vector<int>(lg, 0));
		
		for(int i = 0; i < N; i++) {
			if(i % lg == 0)
				block[i / lg][0] = i;
			block[i / lg][0] = min(block[i / lg][0], i);
		}

		for(int j = 1; j < lg; j++)
			for(int i = 0; i < block.size(); i++)
				block[i][j] = min(block[i][j - 1], block[i + (i + (1 << (j - 1)) < block.size() ? (1 << (j - 1)) : 0)][j - 1]);
		sblock.assign(N, 0);
		std::vector<int> st;
		for(int i = 0; i < block.size(); i++) {
			st.clear();
			for(int j = i * lg; j < N && j < i * lg + lg; j++) {
				while(!st.empty() && data[j] > data[st.back()])
					st.pop_back();
				sblock[j] = 1 << (i * lg + lg - j - 1);
				if(!st.empty())
					sblock[j] |= sblock[st.back()];
				st.push_back(j);
			}
		}
		lookup.assign(1 << lg, 0);
		for(int i = 1, ans = lg - 1; i < (1 << lg); i++) {
			if(1 << (lg - ans) <= i)
				ans--;
			lookup[i] = ans;
		}
	}
	T q(int l, int r) {
		if(r < l)
			swap(l, r);
		int l1 = l / lg + 1;
		int r1 = r / lg - 1;
		int ans = l;
		int t;
		if(l1 <= r1) {
			t = lg - lookup[r1 - l1 + 1] - 1;
			ans = min(ans, min(block[l1][t], block[r1 - (1 << t) + 1][t]));
		}
		t = l1 * lg - 1 < r ? l1 * lg - 1 : r;
		ans = min(ans, lookup[sblock[t] & (~(((1 << (l - (l1 * lg - lg))) - 1) << (l1 * lg - l)))] + l1 * lg - lg);
		t = r;
		l = l > r1 * lg + lg ? l : r1 * lg + lg;
		ans = min(ans, lookup[sblock[t] & (~(((1 << (l - (r1 * lg + lg))) - 1) << (r1 * lg + (lg << 1) - l)))] + r1 * lg + lg);
		// if(!(l<=ans && ans <= r)){
		// 	cout << l << " " << r << " " << ans << endl;
		// }
		assert(0<=ans && ans < data.size());
		return data[ans];
	}
};

void mainmain() {
	int n, m, K;
	cin >> n >> m >> K;

	// assert(n <= 300 && K <= 30);

	vll v(n);
	vll dp(n);
	rep(i, n) {
		cin >> v[i];
		dp[i] = v[i];
	}
	rep(i, K - 1) {
		RMQ<ll> rmq(dp);
		dp = vll(n);
		reep(j, i+1, n) {
			ll t = 0;
			int a = max(j - m, 0);
			int b = j - 1;
			if(a != b) t = rmq.q(a, b);
			else t = rmq.data[a];
			if(t) dp[j] = t + v[j] * (i + 2);
		}
		// if(i==0){
		// 	cout << rmq.q(1,2) << endl;
		// }
		// rep(i,n){
		// 	cout << -dp[i] << " ";
		// }
		// cout<<endl;
	}
	ll ans = 0;
	rep(i, n) {
		maxs(ans, dp[i]);
	}
	cout << ans << endl;
}


signed main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout << fixed << setprecision(20);
	mainmain();
}