input: from typing import List
  
  def min_abs_diff_with_sub_array(nums: List[int], k: int) -> int:
      """
      Given an array nums and an integer k, determine a subarray of nums such that the absolute difference between k and the bitwise OR of the subarray elements is minimized. That is, find a subarray nums[l..r] so that |k - (nums[l] OR nums[l + 1] ... OR nums[r])| is as small as possible.
  
      Return the smallest 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')
      for i in range(len(nums)):
          current_or = 0  # initializes to 0 for each starting point of subarray
          for j in range(i, len(nums)):
              current_or |= nums[j]  # bitwise OR the current value
              current_diff = abs(current_or - k)  # calculate the difference
              if current_diff < min_diff:  # update min_diff if a smaller one is found
                  min_diff = current_diff
      return min_diff