Translating from English to a proposition using predicate calculus

Question

The following sentence needs to be translated from english to a proposition using universal and existential quantifiers.

Everyone in this class knows exactly one person that goes to university.

I have been using the following predicates:

let U = all people

let C(x) = x in this class

let K(x,y) = x knows y

let N (y) = y goes to university

My attempt:

∀x (C(x) ∧ N (y) ∧ K(x,y)

Symbols

I am struggling to denote the exactly one portion and keeping the integrity of the sentence.