A magic index in an array A[0...n-1] is defined to be an index such that A[i] = i. Given a sorted array of integers, write a method to find a magic index, if one exists, in array A. If not, return -1. If there are more than one magic index, return the smallest one.

Example1:

 Input: nums = [0, 2, 3, 4, 5]

 Output: 0

Example2:

 Input: nums = [1, 1, 1]

 Output: 1

Note:

1. 1 <= nums.length <= 1000000
2. This problem is the follow-up of the original problem in the book, i.e. the values are not distinct.