Some More Homework

can someone explain how this solution is formed http://www.codechef.com/viewplaintext/2279326 for A6 Problem - CodeChef problem

Thue-Morse sequence.

Let X be Thue-Morse sequence with length which is a power of 2 and greater than the pattern length.
X’ be flipped X.

All prefixes must lie in :
X,
XX’,
XX’X’X,
XX’X’XX’XXX’

Next the problem can be solved using Z Algorithm