input: from typing import List
  
  def min_bitwise_or_after_operations(nums: List[int], k: int) -> int:
      """
      You are given a 0-indexed integer array nums along with an integer k.
  
      In one operation, you can choose any index i of nums such that 0 <= i < nums.length - 1 and substitute nums[i] and nums[i + 1] with a single occurrence of nums[i] & nums[i + 1], where & denotes the bitwise AND operator.
  
      Return the smallest possible value of the bitwise OR of the remaining elements of nums after performing up to k operations.
  
      Examples:
      >>> nums = [3,5,3,2,7], k = 2
      3
      >>> nums = [7,3,15,14,2,8], k = 4
      2
      >>> nums = [10,7,10,3,9,14,9,4], k = 1
      15
  
      Constraints:
      1 <= nums.length <= 10^5
      0 <= nums[i] < 2^30
      0 <= k < nums.length
      """
output:     while k > 0:
          min_index = -1
          min_value = float('inf')
          for i in range(len(nums) - 1):
              and_value = nums[i] & nums[i + 1]
              if and_value < min_value:
                  min_value = and_value
                  min_index = i
          nums[min_index] = min_value
          nums.pop(min_index + 1)
          k -= 1
      result = 0
      for num in nums:
          result |= num
      return result