404499: GYM101521 C Annoying Mathematics

Dr. Jones is a professor in Byteland Academy who always challenges his students with interesting mathematical problems about constructing sequences.

Today, Dr. Jones takes out R cards with 1, 2, ..., R written on them respectively. Then, he asks his student, Alex, to pick exactly N cards out of R cards in a way such that the lowest common multiple of the N numbers written on the chosen cards is equal to K.

For example, let N = 3, R = 8 and K = 12. The subsets {1, 4, 3} and {2, 3, 4} are examples of valid answer whereas subsets {2, 3, 6} and {1, 6, 12} are not.

As Alex hate mathematics, he is asking for your help. Please help him to find a valid subset. If there are more than one valid subsets, you can output anyone of them.

The first and the only line contains three integers, N, R, K.

1 ≤ N ≤ 10⁵, 1 ≤ R, K ≤ 10⁹

Output N space-separated integers in one line, representing the subset of cards satisfying Dr. Jones' request. If there are more than one arrangement, output any one of them. You may output the numbers in any order.

If there is no arrangement satisfying Dr. Jones' request, output -1.

4 8 8

1 2 4 8

5 6 30

1 2 3 5 6

1 12 13

-1