Given a sorted and rotated array A of N distinct elements which is rotated at some point, and given an element key. The task is to find the index of the given element key in the array A.

Example 1:

Input:
N = 9
A[] = {5, 6, 7, 8, 9, 10, 1, 2, 3}
key = 10
Output:
5
Explanation: 10 is found at index 5.

Example 2:

Input:
N = 4
A[] = {3, 5, 1, 2}
key = 6
Output:
-1
Explanation: There is no element that has value 6.

Your Task:
Complete the function search() which takes an array arr[] and start, end index of the array and the K as input parameters, and returns the answer.

Can you solve it in expected time complexity?

Expected Time Complexity: O(log N).
Expected Auxiliary Space: O(1).

Constraints:
1 ≤ N ≤ 10⁷
0 ≤ A[i] ≤ 10⁸
1 ≤ key ≤ 10⁸