The definition of a language $N$ with alphabet set $\left \{ x \right \}$ is given below:
$N= \{ x^{mp} \mid p > \: 0, \text{where m is a positive integer constant} \}$
The minimum number of states needed in a $\text{DFA}$ to recognize $N$ is _________.
- $p+m$
- $p+1$
- $m+1$
- $2^\left ( p+1 \right )$