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 rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL;
typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll;
template<typename T, typename U> static void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> static void amax(T &x, U y) { if(x < y) x = y; }

template<typename Val, typename Cmp = less<Val> >
struct MonotonicQueue {
	vector<pair<Val, int>> q;
	int head, tail;
	Cmp cmp;
	MonotonicQueue(Cmp cmp = Cmp()) : cmp(cmp) {}
	void init(int n) {
		q.resize(n);
		clear();
	}
	bool empty() const { return head == tail; }
	void clear() {
		head = tail = 0;
	}
	void enque(int i, Val x) {
		while(head < tail && cmp(x, q[tail - 1].first))
			-- tail;
		q[tail ++] = make_pair(x, i);
	}
	void deque(int i) {
		if(head < tail && q[head].second == i)
			++ head;
	}
	Val get() const {
		return q[head].first;
	}
};

int main() {
	int N; int M; int K;
	while(~scanf("%d%d%d", &N, &M, &K)) {
		vector<int> A(N);
		for(int i = 0; i < N; ++ i)
			scanf("%d", &A[i]);
		vector<ll> dp(N);
		rep(i, N)
			dp[i] = A[i];
		rer(k, 2, K) {
			MonotonicQueue<ll, greater<ll>> mq;
			mq.init(N);
			reu(i, k - 2, N) {
				ll x = dp[i];
				mq.deque(i - M - 1);
				if(k - 2 < i)
					dp[i] = (ll)k * A[i] + mq.get();
				mq.enque(i, x);
			}
		}
		ll ans = *max_element(dp.begin(), dp.end());
		printf("%lld\n", ans);
	}
	return 0;
}