$[20\%]$ Suppose that we are using extendible hashing as a secondary index on a table column

that contains the following search$-$key values:

$124,112,82,154,80,51,1,187.$

Assume that the hash function is $h(x)=x$ mod $13$ and each bucket can hold two search$-$key

values and their pointers to the records only, and a maximum of $3$ bits of a hash value are

used. Show the extendable hash structure after insertion of $82,80$ and $187$ if the search

keys are inserted according to the above order.