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;
typedef long long ll;
typedef pair<int, ll> PII;

#define fi first
#define se second
#define mp make_pair
#define pb push_back

#define N 100010
#define K 310
int n, m, k;
ll a[N];

deque<PII> q[K];
ll S = 0;

void add(int x, PII y) {
	while (!q[x].empty() && q[x].back().se < y.se) q[x].pop_back();
	q[x].push_back(y);
}

void clr(int x, int nw) {
	while (!q[x].empty() && q[x].front().fi < nw - m) q[x].pop_front();
}

ll ans(int x) {
	if (q[x].empty()) return -1;
	return q[x].front().se;
}

int main () {
	cin >> n >> m >> k;
	for (int i = 0; i < n; i ++) cin >> a[i];
	for (int i = 0; i < n; i ++) {
		for (int j = k-1; j >= 1; j --) {
			clr(j, i);
			ll s = ans(j);
			if (s != -1) {
				add(j+1, mp(i, s+(ll)(j+1)*a[i]));
			}
		}
		add(1, mp(i, a[i]));
		S = max(S, ans(k));
	}
	
	cout << S << endl;
	return 0;
}