You are given an integer array nums and an integer k.

An integer h is called valid if all values in the array that are strictly greater than h are identical.

For example, if nums = [10, 8, 10, 8], a valid integer is h = 9 because all nums[i] > 9 are equal to 10, but 5 is not a valid integer.

You are allowed to perform the following operation on nums:

Return the minimum number of operations required to make every element in nums equal to k. If it is impossible to make all elements equal to k, return -1.

 

Example 1:

Input: nums = [5,2,5,4,5], k = 2

Output: 2

Explanation:

The operations can be performed in order using valid integers 4 and then 2.

Example 2:

Input: nums = [2,1,2], k = 2

Output: -1

Explanation:

It is impossible to make all the values equal to 2.

Example 3:

Input: nums = [9,7,5,3], k = 1

Output: 4

Explanation:

The operations can be performed using valid integers in the order 7, 5, 3, and 1.

 

Constraints: