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 DEBUG_MODE
#define endl '\n'
#ifdef DEBUG_MODE
#define DEBUG(...) debug_func_mult(split_names(#__VA_ARGS__), __VA_ARGS__)
#define DEBUG_ENDL endl << flush
#define DEBUG_SEPARATOR_LINE cout<<"=================\n"
#else
#define DEBUG(...) 0
#define DEBUG_ENDL 0
#define DEBUG_SEPARATOR_LINE 0
#endif
#define ALL(V) (V).begin(), (V).end()
#define ALLR(V) (V).rbegin(), (V).rend()
#define DEBUG_ENDL_S(S) ((S).size() ? "\n" : "") << flush;

template <typename T> using V = vector<T>;
template <typename T> using VV = V<V<T>>;
template <typename T, typename U> using P = pair<T, U>;
using ll = int64_t;
using PLL = P<ll, ll>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename Head, typename... Tail> const Head& var_min(const Head &head, const Tail&... tail) { return min(head, var_min(tail...)); }
template <typename Head, typename... Tail> const Head& var_max(const Head &head, const Tail&... tail) { return max(head, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }

string to_string(const string &s) { return s; }

template <typename T, typename U>
string to_string(const P<T, U> &p) {
    string ret = "(";
    ret += to_string(p.first);
    ret += ", ";
    ret += to_string(p.second);
    ret += ")";
    return move(ret);
}

template <typename T>
string to_string(const V<T> &v) {
    string ret = "{";
    for(const T &t : v) {
        ret += to_string(t);
        ret += ", ";
    }
    ret += "}";
    return move(ret);
}

template <typename T>
void debug_func(const T &t, const string &s = "") {
    if(s.size()) cout << s << " = ";
    cout << to_string(t) << DEBUG_ENDL_S(s);
}

template <typename T>
void debug_func_mult(int idx, const V<string> &names, const T &t) {
    debug_func(t, names[idx]);
}

template <typename T>
void debug_func_mult(const V<string> &names, const T &t) {
    debug_func(t, names[0]);
}

template <typename Head, typename... Tail>
void debug_func_mult(int idx, const V<string> &names, const Head &head, const Tail&... args) {
    debug_func(head, names[idx]);
    debug_func_mult(idx + 1, names, args...);
}

template <typename Head, typename... Tail>
void debug_func_mult(const V<string> &names, const Head &head, const Tail&... args) {
    debug_func(head, names[0]);
    debug_func_mult(1, names, args...);
}

V<string> split_names(string &&s) {
    replace(ALL(s), ' ', ',');
    V<string> ret;
    istringstream ss(s);
    string t;
    while(getline(ss, t, ',')) if(t.size()) ret.push_back(move(t));
    return move(ret);
}

inline void init_io() {
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(30);
}

int main() {
    init_io();
    ll N, M, K;
    cin >> N >> M >> K;
    V<ll> A(N);
    for(ll &e : A) cin >> e;
    V<ll> ans = A;
    for(ll loops = 1; loops < K; loops++) {
        deque<ll> deq;
        V<ll> nxt(N, 0);
        auto push_deq = [&](ll i) {
            while(deq.size() && ans[deq.back()] <= ans[i]) deq.pop_back();
            deq.push_back(i);
        };
        for(ll i = max<ll>(0, loops - M); i < loops; i++) push_deq(i);
        for(ll i = loops; i < N; i++) {
            while(deq.front() + M < i) deq.pop_front();
            nxt[i] = (loops + 1) * A[i] + ans[deq.front()];
            push_deq(i);
        }
        ans = move(nxt);
    }
    cout << *max_element(ALL(ans)) << endl;
    return 0;
}