Your solution should contain the input, output, pseudocode, and Time$/$space analysis with necessary comments. There is an integer array nums sorted in ascending order $($with distinct values$).$Prior to being passed to your function, nums is possibly rotated at an unknown pivot index k $(1<=$ k $<$ nums.length$)$ such that the resulting array is $[$nums$[$k$],$ nums$[$k$+1],...,$ nums$[$n$-1],$ nums$[0],$ nums$[1],...,$ nums$[$k$-1]](0-$indexed$).$ For example, $[0,1,2,4,5,6,7]$ might be rotated at pivot index $3$ and become $[4,5,6,7,0,1,2].$Given the array nums after the possible rotation and an integer target, return the index of target if it is in nums, or $-1$ if it is not in nums.You must write an algorithm with O$($log n$)$ runtime complexity.

Example $1$:Input: nums $=[4,5,6,7,0,1,2],$ target $=0$Output: $4$

Example $2$:Input: nums $=[4,5,6,7,0,1,2],$ target $=3$Output: $-1$

Example $3$:Input: nums $=[1],$ target $=0$

Output: $-1$