You have studied the $$textbook$$ version of Diffie$-$Hellman key exchange protocol, where all parameters are chosen to be very large, in practice, engineers may try to do all kinds of optimizations to make if faster. Consider the following example: given public parameters: group generator g and a large prime number p$,$ Alice and Bob each choose a random number x$,$y respectively, from $\{1,...,500\},$ and then continue the protocol by sending out gx mod p$,$ gy mod p respectively. One benefit in the $2$ engineer$$s mind is that in this way, they may avoid the heavy modular exponentiation, since now gx$,$gy may not be larger than p thus their original values are good enough $($the same even if after modular p$).$ Is this a secure version of the Diffie$-$Hellman protocol? $($here$,$ we only consider eavesdropping attackers; there is no need to worry about active attacks that may modify those transmitted values yet$).$ Please briefly explain. $(5$ points$)$