class Solution:
  def findNumbers(self, nums, k):
    missing_numbers = []

    # swapping function
    def swap(i, j):
      nums[i], nums[j] = nums[j], nums[i]

    # if number not in position and number is not outside the array boundary and number does not point to number that is correctly positioned  
    for i in range(len(nums)):
      while nums[i] > 0 and nums[i] != i + 1 and nums[i] - 1 < len(nums) and nums[i] != nums[nums[i] - 1]:
        swap(i, nums[i] - 1)

    # find the missing numbers 
    wrong_numbers = set()
    for i in range(len(nums)):
      if nums[i] != i + 1:
        missing_numbers.append(i + 1)
        # add the miss-placed number to the set 
        wrong_numbers.add(nums[i])
        # if we have found all the missing k numbers just return
        if len(missing_numbers) == k:
          return missing_numbers
          
    # figure out remaining numbers
    i = len(nums) + 1
    while len(missing_numbers) < k:
      if i not in wrong_numbers:
        missing_numbers.append(i)
      i += 1

    return missing_numbers