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 <iomanip>
#include <algorithm>
#include <bitset>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <cmath>
#include <time.h>
#include <random>
#include <string>
#include <cassert>
#include <vector>
#include <ostream>
#include <istream>
#include <stack>
#include <deque>
#include <queue>
#include <functional>
#include <chrono>
#include <stack>

using namespace std;

#define int long long
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define pii pair<int, int>
#define ld long double

ostream& operator<< (ostream &out, const vector<int> &b) {
    for (auto k : b) out << k << " ";
    return out;
}

istream& operator>> (istream& in, pii& b) {
    in >> b.first >> b.second;
    return in;
}

ostream& operator<< (ostream& out, const pii& b) {
    out << "{" << b.first << ", " << b.second << "}";
    return out;
}

template <typename T1, typename T2> inline bool chkmin(T1 &x, const T2 &y) {if (x > y) {x = y; return 1;} return 0;}
template <typename T1, typename T2> inline bool chkmax(T1 &x, const T2 &y) {if (x < y) {x = y; return 1;} return 0;}


#ifdef LOCAL
    #define dbg(x) cout << #x << " : " << (x) << "\n";
    const int INF = 1e15;
    // const int mod = 2600000069;
    // const int p = 10;
#else
    #define dbg(x) 57
    const int INF = 1e15;
    // const int mod = 2600000069;
    // const int p = 179;
#endif

const ld PI = acos(-1);

#define time clock() / (double) CLOCKS_PER_SEC

// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC target("sse,sse2,sse3,sse3,sse4")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("fast-math")
// #pragma GCC target("avx2")  
// #pragma GCC optimize("section-anchors")
// #pragma GCC optimize("profile-values,profile-reorder-functions,tracer")
// #pragma GCC optimize("vpt")
// #pragma GCC optimize("rename-registers")
// #pragma GCC optimize("move-loop-invariants")
// #pragma GCC optimize("unswitch-loops")
// #pragma GCC optimize("function-sections")
// #pragma GCC optimize("data-sections")

mt19937 gen(chrono::high_resolution_clock::now().time_since_epoch().count());

const int MAXN = 1e5 + 10;

int RM = -INF;
vector<int> L, R, LM;

void reset() {
    RM = -INF;
    L.clear();
    R.clear();
    LM.clear();
}

void add(int x) {
    R.pb(x);
    chkmax(RM, x);
}

void del() {
    if (!L.empty()) {
        L.pop_back();
        LM.pop_back();
    } else {
        while (!R.empty()) {
            int mx = R.back();
            if (!L.empty()) {
                chkmax(mx, LM.back());
            }
            L.pb(R.back());
            LM.pb(mx);
            R.pop_back();
        }
        RM = -INF;
        L.pop_back();
        LM.pop_back();
    }
}

int ask() {
    assert(!L.empty() || !R.empty());
    int mx = RM;
    if (!L.empty()) {
        chkmax(mx, LM.back());
    }
    return mx;
}

int n, m, k;
int a[MAXN];
int dp[2][MAXN];
int cur = 0;

// void d() {
//     cout << "------------\n";
//     dbg(L);
//     dbg(LM);
//     dbg(R);
//     dbg(RM);
//     cout << "MAX : " << ask() << "\n";
//     cout << "------------\n";
// }

signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cin >> n >> m >> k;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        dp[cur][i] = a[i];
    }
    for (int i = 2; i <= k; i++) {
        cur ^= 1;
        for (int j = 0; j < n; j++) {
            dp[cur][j] = -INF;
        }
        reset();
        for (int j = 1; j < n; j++) {
            add(dp[!cur][j - 1]);
            if (j >= m + 1) { // j - m - 1 >= 0
                del();
            }
            dp[cur][j] = ask() + i * a[j];
        }
    }
    int ans = -INF;
    for (int i = 0; i < n; i++) {
        chkmax(ans, dp[cur][i]);
    }
    cout << ans << "\n";
}
/*

*/