from typing import List


class Solution:
    def bin_specialArray(self, nums: List[int]) -> int:
        nums.sort()
        left, right = 0, len(nums)

        while left <= right:
            mid = (left + right) // 2
            count = sum(1 for num in nums if num >= mid)

            if count == mid:
                return mid
            elif count < mid:
                right = mid - 1
            else:
                left = mid + 1

        return -1

    def specialArray(self, nums: List[int]) -> int:
        """
        Determines if there is a special number x in the list such that there are exactly x elements
        in the list that are greater than or equal to x.

        Args:
            nums (List[int]): The list of non-negative integers.

        Returns:
            int: The special number x, or -1 if no such number exists.
        """
        nums.sort()
        n = len(nums)

        for x in range(1, n + 1):
            # Count how many numbers are greater than or equal to x
            count = sum(1 for num in nums if num >= x)

            if count == x:
                return x

        return -1