Consider the language D $=\{$a$^$m b$^$n where n $>$ m$\}.$

$1)$ Use the pumping lemma to show that D is not a regular language. Hint: Choose s such that s has a number of $\text{'}$b$\text{'}$s that's one more than the number of $\text{'}$a$\text{'}$s$.$ By the way, a common error is to set p to some value you choose like $2.$ You can't choose the pumping length, it's something that would depend on the particular DFA used to recognize L$.$ All you know is that p exists and is some positive integer.

$2)$ Draw the state diagram for a PDA that recognizes D$.$ Your PDA must match the version used in Sipser, not from any other source.