$($c$)$ Integers are inserted into a hash table $H[1$dots$13]$ using "open addressing with double hashing". The primary hash function is $h_1(k)=1+k\%13.$ The secondary hash function is $h_2(k)=1+k\%9.$ Show the state of the array after inserting, in order, the keys $31,22,17,25,28,30,34,15,39,42.$ If a calculated location is greater than $13,$ subtract $13$ to get a valid location. For example, $18$ converts to $5.$

$[4]$