Problem:
Score : 700 points

Problem Statement

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}

Partial Scores

In the test set worth 100 points, M = N.

In the test set worth another 200 points, N ≦ 300 and K ≦ 30.

In the test set worth another 300 points, K ≦ 30.

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.

Sample Input 1

5 2 3
10 2 8 10 2

Sample Output 1

56

The total score is maximized when panels 1,3 and 4 are hit, in this order.

Sample Input 2

5 5 2
5 2 10 5 9

Sample Output 2

28

This case satisfies the additional constraint M = N for a partial score.

Sample Input 3

10 3 5
3 7 2 6 9 4 8 5 1 1000000000

Sample Output 3

5000000078

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#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 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<class T> class RMQ {
public:
	vector<T> data;
	vector<vector<int> > block;
	vector<int> sblock;
	int N;
	int lg;
	// Max -> data[b] > data[a]
	int argMin(int a, int b) {
		return data[b] < data[a] ? b : a;
	}
	// x の下位 y bit を 0 にする
	int maskBits(int x, int y) {
		return (x >> y) << y;
	}
	RMQ(vector<T> &v) {
		data = v;
		N = data.size();

		lg = 32 - __builtin_clz(N);
		// lg = 32;

		block.assign((N + lg - 1) / lg, vector<int>(lg, 0));

		for(int i = 0; i < N; i++) {
			if(i % lg == 0) block[i / lg][0] = i;
			block[i / lg][0] = argMin(block[i / lg][0], i);
		}

		for(int j = 1; j < lg; j++) {
			for(int i = 0; i < block.size(); i++) {
                block[i][j] = argMin(block[i][j - 1], block[i + (1 << (j - 1)) < block.size() ? i + (1 << (j - 1)) : block.size() - 1][j - 1]);
				// block[i][j] = argMin(block[i][j - 1], block[min(i + (1 << (j - 1)), (int)block.size() - 1)][j - 1]);
			}
		}

		sblock.assign(N, 0);
		stack<int> st;
		for(int i = 0; i < N; i++) {
			if(i % lg == 0) while(st.size()) st.pop();
			while(st.size() && i == argMin(i, st.top())) st.pop();
			if(st.size()) {
				int g = st.top();
				sblock[i] = sblock[g] | (1 << (g % lg));
			}
			st.push(i);
		}
	}
	// return = min{data[i] : i in [l .. r]}
	T query(int l, int r) {
		if(l == r) return data[l];
		int l1 = l / lg + 1;
		int r1 = r / lg - 1;
		int ret = l;
		if(l1 <= r1) {
			int d = r1 - l1 + 1;
			if(d <= 2){
				ret = argMin(ret, argMin(block[l1][0], block[r1][0]));
			}
			else {
				int lg2 = 32 - __builtin_clz(d) - 1;
				ret = argMin(ret, argMin(block[l1][lg2], block[r1 - (1 << lg2)+1][lg2]));
			}
		}
		if(l1 - r1 == 2) { // same block
			int t = maskBits(sblock[r], l % lg);
			if(t == 0) {
				ret = argMin(ret, r);
			}
			else {
				ret = argMin(ret, __builtin_ctz(t) + (l1 - 1) * lg);
			}
		}
		else { // other block
			int t1 = maskBits(sblock[l1 * lg - 1], l % lg);
			if(t1 == 0) {
				ret = argMin(ret, l1 * lg - 1);
			}
			else {
				ret = argMin(ret, __builtin_ctz(t1) + (l1 - 1) * lg);
			}
			int t2 = sblock[r];
			if(t2 == 0) {
				ret = argMin(ret, r);
			}
			else {
				ret = argMin(ret, __builtin_ctz(t2) + (r1 + 1) * lg);
			}
		}
		return data[ret];
	}
};

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;
			t = rmq.query(a, b);
			if(t) dp[j] = t + v[j] * (i + 2);
		}
		// 3 7 2 6 9 4 8 5 1 1000000000
		// if(i==0){
		// 	cout << -rmq.query(1,2) << endl;
		// }
		// rep(i,n){
		// 	rep(j,i+1){
		// 		cout<<j<<" "<<i<<" "<<-rmq.query(j,i)<<endl;
		// 	}
		// }
		// break;
		// rep(j,n){
		// 	cout << -dp[j] << " ";
		// }
		// 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();
}