Hello!

The problem is about this problem: 239C - Not Wool Sequences :)

I couldn't solve this problem during the contest. So today I decided to look back at the problem once more to see whether I could solve it. But I couldn't and read its editorial.

I denote XOR by

The editorial states that for every sequence a ,

a₁, a₂, ..., a_n

we can create a sequence b,

b₀, b₁, b₂, ..., b_n

which is defined by :

b₀ = 0

and hence

Since

all b_i are distinct integers within range 0... 2^m - 1 , or something like that.

So we count the number of such b and that is our answer.

Now my question is that, the above reasoning means that there must exist a bijective relationship between all a and all b.

Is it true that for each such a there always exists a unique b ?

I couldn't understand this part so I asked you all about this. Thank you!