input: from typing import List
  from collections import Counter
  
  def find_largest_valid_subarray(nums: List[int]) -> int:
      """
      Given an array of positive integers nums, the task is to pick a subset that adheres to the following rule:
  
      The subset must be able to be organized into a 0-indexed sequence that follows the pattern: [x, x2, x4, ..., xk/2, xk, xk/2, ..., x4, x2, x] (where k can be any non-negative power of 2). For instance, [2, 4, 16, 4, 2] and [3, 9, 3] conform to the pattern, whereas [2, 4, 8, 4, 2] does not.
  
      Return the maximum size of a subset fulfilling these guidelines.
  
      Examples:
      >>> nums = [5,4,1,2,2]
      3
      >>> nums = [1,3,2,4]
      1
  
      Constraints:
      2 <= nums.length <= 10^5
      1 <= nums[i] <= 10^9
      """
output:     
      freq = Counter(nums)
      
      def is_valid(middle, counts):
          base = counts[middle]
          left, right = base, base
          factor = 2
  
          while middle * factor in counts:
              if counts[middle * factor] < left:
                  return False
              left = counts[middle * factor]
              factor *= 2
  
          factor = 2
          while middle / factor in counts:
              if counts[middle / factor] < right:
                  return False
              right = counts[middle / factor]
              factor *= 2
  
          return True
  
      max_size = 0
  
      for num in freq:
          if is_valid(num, freq):
              valid_size = sum(freq[n] for n in freq if n % num == 0 and (n // num) & (n // num - 1) == 0)
              max_size = max(max_size, valid_size)
  
      return max_size
  