Liebig's Barrels

2000ms

262144K

Description:

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.

$\text{[math]}$

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.

Input:

The first line contains three space-separated integers n, k and l (1 ≤ n, k ≤ 10⁵, 1 ≤ n·k ≤ 10⁵, 0 ≤ l ≤ 10⁹).

The second line contains m = n·k space-separated integers a₁, a₂, ..., a_m (1 ≤ a_i ≤ 10⁹) — lengths of staves.

Output:

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.

Sample Input:

4 2 1
2 2 1 2 3 2 2 3

Sample Output:

Sample Input:

2 1 0
10 10

Sample Output:

Sample Input:

1 2 1
5 2

Sample Output:

Sample Input:

3 2 1
1 2 3 4 5 6

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF985C