divide-and-conquer algorithm

An ๐‘™-subarray of ๐‘‹ is
any sequence of ๐‘™ consecutive elements of the array ๐‘‹. The trough of an ๐‘™-subarray is the
minimum value in that ๐‘™-subarray. Give a divide-and-conquer algorithm that takes as input an
array ๐‘‹[1: ๐‘›] and a positive integer ๐‘™ โ‰ค ๐‘›, and returns the starting position of the ๐‘™-subarray that
has the largest trough. Analyze the time complexity of your algorithm in terms of ๐‘› and ๐‘™. (Your
algorithm should split the input into two halves)