There are nn emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The ii-th emote increases the opponent's happiness by ai units (we all know that emotes in this game are used to make opponents happy).

You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than kk times in a row (otherwise the opponent will think that you're trolling him).

Note that two emotes i and j (i≠j) such that ai=aj are considered different.

You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness.

Input

The first line of the input contains three integers n,mn,m and kk (2≤n≤2⋅105, 1≤k≤m≤2⋅109) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row.

The second line of the input contains nn integers a1,a2,…,an (1≤ai≤109), where aiai is value of the happiness of the ii-th emote.

Output

Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement.

Examples

input

Copy

6 9 21 3 3 7 4 2

output

Copy

54

input

Copy

3 1000000000 11000000000 987654321 1000000000

output

Copy

1000000000000000000

 

#include 
          
           using namespace std;long long a[200005];bool cmp(long long a,long long b){    return a>b;}int main(){    long long n,m,k,maxx=0,maxi=0;    cin>>n>>m>>k;    int i;    for(i=0;i
           
            >a[i];        if(a[i]>maxx){            maxi=maxx;            maxx=a[i];        }        else {            if(a[i]>maxi) maxi=a[i];        }    }//    cout<
            
             <<" "<
             
              <
              
               0;m--){        if(flag