Lexicographically Smallest Permutation Greater Than Target

Description

You are given two strings s and target, both having length n, consisting of lowercase English letters.

Return the lexicographically smallest permutation of s that is strictly greater than target. If no permutation of s is lexicographically strictly greater than target, return an empty string.

A string a is lexicographically strictly greater than a string b (of the same length) if in the first position where a and b differ, string a has a letter that appears later in the alphabet than the corresponding letter in b.