Consider a simple linear congruential generator $($LCG$)$ with the following parameters:

Xn$+1=($a $.$ Xn $+$ c$)$ mod m

The PRNG is defined as follows

a$=5$

c$=3$

m$=16$

X$0=2($the seed$)$

a$.$ Calculate the first four values generated by the LCG$.$ Show the step$-$by$-$step calculations. $(4$ points$)$

b$.$ Analyze the sequence of generated numbers and determine the period of the PRNG$.$ Explain how you arrived at this conclusion. $(3$ points$)$