CF632E Thief in a Shop

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.

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