A hash table contains $1000$ slots, indexed from $1$ to $1000.$ The elements stored in the table have keys that range in value from $1$ to $99999.$ Which of the following hash functions would work correctly? And explain why.

$($a$)$ Key MOD $1000$

$($b$)($Key$-1)$ MOD $1000$

$($c$)(($Key$+1)$ MOD $999)$

$($d$)($Key MOD $1000)+1$