A spy lives in a city of n$=2^$k$,$ k$>=0,$ residents. All residents, including the spy$,$ do not lie.

Your task is to find the spy by asking the residents the question: $"$Is there a spy among you?".

If you are asking the question to a group of more than one person, you will get one answer not multiple answers.

a$.$ Design a decrease and conquer algorithm to find the spy as quickly as possible.

b$.$ What is the basic operation of your algorithm?

c$.$ Show and simplify an expression for the number of times the basic operation is performed in the worst case. Show the steps in your answer.

d$.$ What variation of decrease and conquer is your algorithm? If it is not variable decrease, indicate the constant or the constant factor.