Please show work and provide and explanation

[5 points =4+1 points] Suppose we would like to insert a sequence of numbers into a hash table with table size 8 using the two open addressing methods: linear probing and double hashing. The primary hash function is h1(k)=kmod8, and the secondary hash function is h2(k)=1+(kmod7). Linear probing function would then be h(k,i)=(h1(k)+i)mod8 Double hashing function would then be h(k,i)=(h1(k)+ih2(k))mod8 a. [4 points] If the sequence of keys is , please successively insert these keys into the following table. Show each collision with an x in the table slot along with the key that is stored in the slot. b. [1 points] For the hashing functions and table size we used in part (a), does the linear probing fully utilize the table? How about double hashing