input: from typing import List
  
  def minimize_abs_difference(nums: List[int], k: int) -> int:
      """
      Given an array nums and an integer k, find a subarray of nums where the absolute difference between k and the bitwise OR of the subarray elements is minimized. Specifically, choose a subarray nums[l..r] such that |k - (nums[l] OR nums[l + 1] ... OR nums[r])| is minimized.
  
      Return the smallest possible value of this 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')
      n = len(nums)
  
      for i in range(n):
          current_or = 0
          for j in range(i, n):
              current_or |= nums[j]
              min_diff = min(min_diff, abs(k - current_or))
              # If we find a subarray which makes the difference zero, we can return immediately
              if min_diff == 0:
                  return 0
  
      return min_diff