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 <iostream>
#include <fstream>
#include <sstream>

#include <vector>
#include <set>
#include <bitset>
#include <map>
#include <deque>
#include <string>

#include <algorithm>
#include <numeric>

#include <cstdio>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cmath>

#define pb push_back
#define pbk pop_back
#define mp make_pair
#define fs first
#define sc second
#define all(x) (x).begin(), (x).end()
#define foreach(i, a) for (__typeof((a).begin()) i = (a).begin(); i != (a).end(); ++i)
#define len(a) ((int) (a).size())

#ifdef CUTEBMAING
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define eprintf(...) 42
#endif

#define rank hurank

using namespace std;

typedef long long int64;
typedef long double ld;
typedef unsigned long long lint;

const int inf = (1 << 30) - 1;
const int64 linf = (1ll << 62) - 1;
const int N = 1e6 + 100;

int n, m, k;
int a[N];

int64 dp[N];

int parent[N], rank[N];
int64 value[N];

inline int findSet(int v) {
    if (parent[v] != v) {
        return parent[v] = findSet(parent[v]);
    }
    return v;
}

inline void unite(int a, int b) {
    a = findSet(a);
    b = findSet(b);
    if (a == b) {
        return ;
    }
    if (rank[a] == rank[b]) {
        rank[a]++;
    }
    if (rank[a] > rank[b]) {
        swap(a, b);
    }
    parent[a] = b;
}

int main() {
#ifdef XCODE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    cin >> n >> m >> k;
    for (int i = 0; i < n; i++) {
        scanf("%d", &a[i]);
    }
    for (int i = 0; i < k; i++) {
        for (int j = n - 1; j >= 0; j--) {
            dp[j + 1] = dp[j];
        }
        dp[0] = i == 0 ? 0 : -linf;
        for (int j = 0; j < n; j++) {
            parent[j] = j;
            rank[j] = 0;
        }
        vector<pair<int64, int>> stack;
        for (int j = 0; j < n; j++) {
            pair<int64, int> curValue(dp[j] + 1ll * (i + 1) * a[j], j);
            while (len(stack) > 0 && stack.back().fs <= curValue.fs) {
                unite(stack.back().sc, curValue.sc);
                stack.pbk();
            }
            value[findSet(curValue.sc)] = curValue.fs;
            stack.pb(curValue);
            dp[j] = value[findSet(max(0, j - m + 1))];
        }
    }
    cout << *max_element(dp, dp + n) << endl;
    return 0;
}