You have an array A[0], A[1], ..., A[n - 1] of distinct integers that has the following property:The values in the array increase up to index p for some p between 0 and n - 1, and then decrease for all indices beyond p through position n-1.You want to find the p index at which the peak value occurs. Describe a divide-and-conquer algorithm that can solve this problem in?(lg n) time, where the work unit is comparison of array values. Do a formal analysis to prove this. you can assume that n is a power of 2.