You are given a palindromic string s and an integer k.

Return the k-th lexicographically smallest palindromic permutation of s. If there are fewer than k distinct palindromic permutations, return an empty string.

Note: Different rearrangements that yield the same palindromic string are considered identical and are counted once.

Example 1:

Input: s = "abba", k = 2

Output: "baab"

Explanation:

The two distinct palindromic rearrangements of "abba" are "abba" and "baab".
Lexicographically, "abba" comes before "baab". Since k = 2, the output is "baab".

Example 2:

Input: s = "aa", k = 2

Output: ""

Explanation:

There is only one palindromic rearrangement: "aa".
The output is an empty string since k = 2 exceeds the number of possible rearrangements.

Example 3:

Input: s = "bacab", k = 1

Output: "abcba"

Explanation:

The two distinct palindromic rearrangements of "bacab" are "abcba" and "bacab".
Lexicographically, "abcba" comes before "bacab". Since k = 1, the output is "abcba".

Constraints:

1 <= s.length <= 10⁴
s consists of lowercase English letters.
s is guaranteed to be palindromic.
1 <= k <= 10⁶