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