Shortest and Lexicographically Smallest Beautiful String

You are given a binary string s and a positive integer k.

A substring of s is beautiful if the number of 1's in it is exactly k.

Let len be the length of the shortest beautiful substring.

Return the lexicographically smallest beautiful substring of string s with length equal to len. If s doesn't contain a beautiful substring, return an empty string.

A string a is lexicographically larger than a string b of the same length if, in the first position where a and b differ, a has a character strictly larger than the corresponding character in b.