Problem Statement:

Let$$s think you are playing with numbers. You have been given a set of integers as $$candidate

numbers$$ and an integer as a $$query number$.$ Now, count the number of $1$s $(1$s count value$)$ in

the binary representations of all the candidate and query numbers. Then, you have to figure out

two numbers from the candidate numbers$$ set$-$

I. One number$$s $1$s count value$$ must have a minimum difference from the $1$s count

value$$ of the query number.

II$.$ Another number$$s $1$s count value$$ must have a maximum difference from the $1$s count

value$$ of the query number.

If you find multiple candidate numbers with minimum differences, choose the lowest number

among them. Again, if multiple numbers can be identified with maximum differences, consider

the highest number among them.

Input:

Take an integer n $(1<=$ n $<=1000)$ as input, representing the total test cases.

Each case starts with a positive integer k $(1<=$ k $<4,294,967,296)$ indicating the query

number and an integer m $(3<=$ m $<=10000)$ representing how many integer numbers are in the

set of $$candidate numbers$.$ The next line contains m positive integer numbers separated by

white spaces. Those integers represent the elements of the candidate numbers$$ set, and each

number will be between $1$ and $4,294,967,295.$

Output:

Output should be organized as in the sample shown on the next page. For each test case, you

must show the case number at the beginning. Then, $($m$+1)$ lines will show the binary

representations of the candidate numbers and the query number in $32$ bits. Finally, print two

desired numbers $($stated in the $$Problem Statement$$ section$)$ as output.

Restrictions:

You cannot use one$/$multi$-$dimensional arrays or any other data structures. You also cannot call any selfimplemented or built in founctions excepts scanf and printf