We have a database file with $14,000,000$ pages. we want to sort the file using external merge sort. Assume that the DBMS is not using double buffering, and that it uses quicksort for in$-$memory sorting. Let B denote the number of buffers. What is the smallest value of B that the DBMS can sort the target file using only $8$ passes?

options:

$7$

$8$

$9$

$2450$

$2451$

$2452$

$3742$

$3743$