Determine if a number is a 'happy number'. A happy number eventually reaches 1 when replaced by the sum of the squares of its digits, repeating the process until it does.

Given a number n and an integer k, find the kth lexicographical permutation of the sequence 1, 2, ..., n. Essentially, you need to generate the kth permutation without explicitly calculating all the preceding permutations.

Find the largest subset of numbers in an array where the bitwise AND of all numbers in the subset is greater than zero. Return the size of this largest subset.