input: from typing import List
  
  def diff_between_k_and_sub_array(nums: List[int], k: int) -> int:
      """
      You are given an array nums and an integer k. You need to find a subarray of nums such that the absolute difference between k and the bitwise OR of the subarray elements is as small as possible. In other words, select a subarray nums[l..r] such that |k - (nums[l] OR nums[l + 1] ... OR nums[r])| is minimum.
  
      Return the minimum possible value of the absolute difference.
  
      A subarray is a contiguous non-empty sequence of elements within an array.
  
      Examples:
      >>> nums = [1,2,4,5], k = 3
      0
      >>> nums = [1,3,1,3], k = 2
      1
  
      Constraints:
      1 <= nums.length <= 10^5
      1 <= nums[i] <= 10^9
      1 <= k <= 10^9
      """
  
output: 
      min_diff = float('inf')
      current_or = 0
      
      for num in nums:
          current_or |= num
          min_diff = min(min_diff, abs(k - current_or))
      
      return min_diff
  