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:
// {{{ by shik
#include <bits/stdc++.h>
#include <unistd.h>
#define SZ(x) ((int)(x).size())
#define ALL(x) begin(x),end(x)
#define REP(i,n) for ( int i=0; i<int(n); i++ )
#define REP1(i,a,b) for ( int i=(a); i<=int(b); i++ )
#define FOR(it,c) for ( auto it=(c).begin(); it!=(c).end(); it++ )
#define MP make_pair
#define PB push_back
using namespace std;
typedef long long LL;
typedef pair<int,int> PII;
typedef vector<int> VI;

#ifdef SHIK
template<typename T>
void _dump( const char* s, T&& head ) { cerr<<s<<"="<<head<<endl; }

template<typename T, typename... Args>
void _dump( const char* s, T&& head, Args&&... tail ) {
    int c=0;
    while ( *s!=',' || c!=0 ) {
        if ( *s=='(' || *s=='[' || *s=='{' ) c++;
        if ( *s==')' || *s==']' || *s=='}' ) c--;
        cerr<<*s++;
    }
    cerr<<"="<<head<<", ";
    _dump(s+1,tail...);
}

#define dump(...) do { \
    fprintf(stderr, "%s:%d - ", __PRETTY_FUNCTION__, __LINE__); \
    _dump(#__VA_ARGS__, __VA_ARGS__); \
} while (0)

template<typename Iter>
ostream& _out( ostream &s, Iter b, Iter e ) {
    s<<"[";
    for ( auto it=b; it!=e; it++ ) s<<(it==b?"":" ")<<*it;
    s<<"]";
    return s;
}

template<typename A, typename B>
ostream& operator <<( ostream &s, const pair<A,B> &p ) { return s<<"("<<p.first<<","<<p.second<<")"; }
template<typename T>
ostream& operator <<( ostream &s, const vector<T> &c ) { return _out(s,ALL(c)); }
template<typename T, size_t N>
ostream& operator <<( ostream &s, const array<T,N> &c ) { return _out(s,ALL(c)); }
template<typename T>
ostream& operator <<( ostream &s, const set<T> &c ) { return _out(s,ALL(c)); }
template<typename A, typename B>
ostream& operator <<( ostream &s, const map<A,B> &c ) { return _out(s,ALL(c)); }
#else
#define dump(...)
#endif

template<typename T>
void _R( T &x ) { cin>>x; }
void _R( int &x ) { scanf("%d",&x); }
void _R( long long &x ) { scanf("%" PRId64,&x); }
void _R( double &x ) { scanf("%lf",&x); }
void _R( char &x ) { scanf(" %c",&x); }
void _R( char *x ) { scanf("%s",x); }

void R() {}
template<typename T, typename... U>
void R( T& head, U&... tail ) {
    _R(head);
    R(tail...);
}

template<typename T>
void _W( const T &x ) { cout<<x; }
void _W( const int &x ) { printf("%d",x); }
template<typename T>
void _W( const vector<T> &x ) {
    for ( auto i=x.cbegin(); i!=x.cend(); i++ ) {
        if ( i!=x.cbegin() ) putchar(' ');
        _W(*i);
    }
}

void W() {}
template<typename T, typename... U>
void W( const T& head, const U&... tail ) {
    _W(head);
    putchar(sizeof...(tail)?' ':'\n');
    W(tail...);
}

#ifdef SHIK
#define FILEIO(...)
#else
#define FILEIO(name) do {\
    freopen(name ".in","r",stdin); \
    freopen(name ".out","w",stdout); \
} while (0)
#endif

// }}}

const int N=1e5+10;
const LL INF=9e18;

int n,m,t;
LL a[N],dp[N],ndp[N];
int main() {
    R(n,m,t);
    REP1(i,1,n) R(a[i]);
    // REP1(i,1,n) dp[i]=-INF;
    REP1(i,1,t) {
        REP1(j,0,n) if ( dp[j]<0 ) dp[j]=-INF;
        deque<pair<LL,int>> q;
        q.push_back({dp[0],0});
        REP1(j,1,n) {
            while ( !q.empty() && q.front().second<j-m ) q.pop_front();
            // LL mx=*max_element(dp+max(0,j-m),dp+j);
            LL mx=q.front().first;
            ndp[j]=mx+i*a[j];
            while ( !q.empty() && q.back().first<=dp[j] ) q.pop_back();
            q.push_back({dp[j],j});
        }
        ndp[0]=-INF;
        memcpy(dp,ndp,sizeof(dp));
    }
    dump(vector<LL>(dp,dp+n));
    LL ans=*max_element(dp+1,dp+n+1);
    assert(ans>0);
    W(ans);
    return 0;
}