Prove that the following two languages are in the class NP$.$ Which of these is in P$?$ Which of them is in coNP?

$P_1=\{$G$|$G is an undirected graph with a cycle on exactly $100$ vertices.$\}$

$P_2=\{($G$,$ k$)|$k is a positive integer and G is an undirected graph with a cycle on exactly k vertices$\}$