A11837. Liebig's Barrels

You have $m=n·k$ wooden staves. The $i$ -th stave has length $a_{i}$ . You have to assemble $n$ barrels consisting of $k$ staves each, you can use any $k$ staves to construct a barrel. Each stave must belong to exactly one barrel.

Let volume $v_{j}$ of barrel $j$ be equal to the length of the minimal stave in it.

You want to assemble exactly $n$ barrels with the maximal total sum of volumes. But you have to make them equal enough, so a difference between volumes of any pair of the resulting barrels must not exceed $l$ , i.e. $|v_{x}-v_{y}|<=l$ for any $1<=x<=n$ and $1<=y<=n$ .

Print maximal total sum of volumes of equal enough barrels or $0$ if it's impossible to satisfy the condition above.

The first line contains three space-separated integers $n$ , $k$ and $l$ ( $1<=n,k<=10^{5}$ , $1<=n·k<=10^{5}$ , $0<=l<=10^{9}$ ).

The second line contains $m=n·k$ space-separated integers $a_{1},a_{2},...,a_{m}$ ( $1<=a_{i}<=10^{9}$ ) — lengths of staves.

Print single integer — maximal total sum of the volumes of barrels or $0$ if it's impossible to construct exactly $n$ barrels satisfying the condition $|v_{x}-v_{y}|<=l$ for any $1<=x<=n$ and $1<=y<=n$ .

In the first example you can form the following barrels: $[1,2]$ , $[2,2]$ , $[2,3]$ , $[2,3]$ .

In the second example you can form the following barrels: $[10]$ , $[10]$ .

In the third example you can form the following barrels: $[2,5]$ .

In the fourth example difference between volumes of barrels in any partition is at least $2$ so it is impossible to make barrels equal enough.