$[28$ pts$.]$ Draw the $7-$entry hash table, by filling out the table below with index values

$0,1,2,$dots,$6("$index$"$ column $1),$ that results from using hash function

$h(k)=|5k+3|mod7$

and the corresponding collision mechanism $($columns $2-5),$ to hash the following seven keys:

$12,10,3,21,6,7,17.$ For each corresponding column, other than the first column, collisions

are handled by $(1)$ chaining $("$chaining$"$ column$),(2)$ linear probing $("$linear$"$ column$),(3)$

quadratic probing $("$quadratic$"$ column$),$ up to the point where the method fails, and $(4)$

double hashing using the secondary hash function

$h^{\text{'}}(k)=q-(kmodq)$

for $q=3("$double$,q=3"$ column$).$