Thief in a Shop

5000ms

524288K

Description:

A thief made his way to a shop.

As usual he has his lucky knapsack with him. The knapsack can contain k objects. There are n kinds of products in the shop and an infinite number of products of each kind. The cost of one product of kind i is a_i.

The thief is greedy, so he will take exactly k products (it's possible for some kinds to take several products of that kind).

Find all the possible total costs of products the thief can nick into his knapsack.

Input:

The first line contains two integers n and k (1 ≤ n, k ≤ 1000) — the number of kinds of products and the number of products the thief will take.

The second line contains n integers a_i (1 ≤ a_i ≤ 1000) — the costs of products for kinds from 1 to n.

Output:

Print the only line with all the possible total costs of stolen products, separated by a space. The numbers should be printed in the ascending order.

Sample Input:

3 2
1 2 3

Sample Output:

2 3 4 5 6

Sample Input:

5 5
1 1 1 1 1

Sample Output:

Sample Input:

3 3
3 5 11

Sample Output:

9 11 13 15 17 19 21 25 27 33

Informação

Provedor Codeforces

Código CF632E