Let's look at the AMSCO cipher. This is a positional cipher with exchanges. You can easily encode or decode a message with a pen and paper, that is of course, if you know the key.

The key is represented as a number that consist of unique digits from 1 to N. N is a length of the key. To encode message we should write a message in a matrix with N columns. The matrix is written row by row. In this process, one or two characters are alternately recorded in a field. One or two characters alternate in rows and in columns too (like a chessboard). The first element is single letter field (this is the arrangement for this mission). The last field can have single characters if there are not enough. Columns are then numbered with digits from the key in order. For example: using the key 312, the first column will be 3, the second is 1 and the third is 2. Lastly, you will write all characters in the columns as they were numbered in the most recent step. All white spaces and punctuation symbols are excluded while letters are in lowercase.

Let's look at this with an example. The message "Lorem ipsum dolor sit amet". And the key is 4123. The cut message is "loremipsumdolorsitamet". In matrix form it will be:

   4   1   2   3
   l  or   e  mi
  ps   u  md   o
   l  or   s  it
  am   e   t

Now write the columns as they are numbered in the ascending order - "oruore", "emdst", "mioit", "lpslam". The encoded message is "oruoreemdstmioitlpslam".

You are given an encoded message and the key. Your mission is to decode the message. Of course in the cut version.

Input: Two arguments. A message as a string (unicode) and a key as an integer.

Output: The decoded message as a string.

decode_amsco("oruoreemdstmioitlpslam", 4123) == "loremipsumdolorsitamet"

    

How it is used: For any cipher, it is important to realize both parts - encoding and decoding. This way, even if you know only one part of the cipher, you can finalize an implementation.

Precondition: 4 ≤ len(str(key))
int(len(str(key)) * 1.5) ≤ len(message)
re.match("\w+$", message)