Parrots

fYanee is a bird enthusiast. Since reading about IP over Avian Carriers (IPoAC), she has spent much of her time training a flock of intelligent parrots to carry messages over long distances.

Yanee's dream is to use her birds to send a message M to a land far far away. Her message M is a sequence of N (not necessarily distinct) integers, each between 0 and 255, inclusive. Yanee keeps K specially-trained parrots. All the parrots look the same, so Yanee cannot tell them apart. Each bird can remember a single integer between 0 and R, inclusive.

Early on, she tried a simple scheme. To send a message, Yanee carefully let the birds out of the cage one by one. Before each bird soared into the air, she taught it a number from the message sequence, in order. Unfortunately, this scheme did not work. Eventually, all the birds did arrive at the destination, but they did not necessarily arrive in the order in which they left. With this scheme, Yanee could recover all the numbers she sent, but she was unable to put them into the right order.

To realize her dream, Yanee needs a better scheme, and for that she needs your help. Given a message M, she plans to let the birds out one by one, as before. She needs you to write a program that performs two separate operations:

• First, the program reads a message M and transforms it into a sequence of at most K integers between 0 and R. Yanee teaches these integers to the birds.
• Second, the program reads the list of integers between 0 and R received as the birds reach their destination, and transforms it back into the original message M.

You may assume that all parrots always arrive at the destination, and that each of them remembers the number it was assigned. Yanee reminds you once again that the parrots may arrive in any order. Note that Yanee only has K parrots, so the sequence of integers between 0 and R that you produce must contain at most K integers.