A happy string is a string that:

- consists only of letters of the set `['a', 'b', 'c']`.
- `s[i] != s[i + 1]` for all values of `i` from `1` to `s.length - 1` (string is 1-indexed).

For example, strings "abc", "ac", "b" and "abcbabcbcb" are all happy strings and strings "aa", "baa" and "ababbc" are not happy strings.

Given two integers `n` and `k`, consider a list of all happy strings of length `n` sorted in lexicographical order.

Return the kth string of this list or return an empty string if there are less than `k` happy strings of length `n`.

Example 1:

    Input: n = 1, k = 3
    Output: "c"
    Explanation: The list ["a", "b", "c"] contains all happy strings of length 1. The third string is "c".

Example 2:

    Input: n = 1, k = 4
    Output: ""
    Explanation: There are only 3 happy strings of length 1.

Example 3:

    Input: n = 3, k = 9
    Output: "cab"
    Explanation: There are 12 different happy string of length 3 ["aba", "abc", "aca", "acb", "bab", "bac", "bca", "bcb", "cab", "cac", "cba", "cbc"]. You will find the 9th string = "cab"

Constraints:

- `1 <= n <= 10`
- `1 <= k <= 100`