@Blastoise firstly, read:

• List of Copies of An Object (Read especially the second answer by Luper. Also list is also an object: everything in Python is pretty much an object.)
• Simply Copying a List is A Problem (in fact see someone's complaint here)

The basic idea is Python copies references. So, the way we initialize M in our code is a big problem: because later we are going to modify it element by element.
Try this in the interactive shell:

>> M = [[0]*3]*4
>> M
>> M[1][2] = 99
>> M

Here, we try to update the third (index 2) element of only the second list copy (index 1) of list of lists M. But since these copies are not true copies, we update third element of every copy, i,e. every list member of M.
The answers above will help you fix this. Make sure your idea works for the above short example with M first, before trying. Good luck! :)