Welcome to Sevenkplus' perfect math class! In this class, you will learn about representation theory. And this class is in a different format than before: Learning by doing! You need to solve a problem, which can be solved elegantly using (really elementary) representation theory. (Of course you can solve this problem without representation theory. But learning more is helpful!)
Sevenkplus had an complex matrix . He calculated and found that . (For a square matrix , is the trace of . is the identity matrix.)
However, the dark side of the world destroyed , and only remained.
Sevenkplus wants to recover his beloved . However, this is impossible.
Nevertheless, doing something weaker is possible: Only recover the eigenvalues of . Here the eigenvalues are defined to be the entries on the diagonal of the Jordan normal form of . For a fixed , they are unique up to permutation.
The first line contains two space separated integers, and .
Followed by lines where for each value of line contains two real numbers , which means that , where is the imaginary unit.
It is guaranteed that there is an that satisfies the relations.
Print lines where for each value of line contains two real numbers .
The multi-set of should be the multi-set of eigenvalues of .
You can output the eigenvalues in any order.
In case of multiple answers output any of them, your answer is considered correct if your answer satisfies the input, within absolute error .
Two possible 's are and . Note that there may be other 's that satisfies the relations.